機械学習の特徴選択戦略11選まとめ！

特徴が多すぎるとモデルの複雑さが増し、過学習が発生します。一方、特徴が少なすぎるとモデルの過小学習が発生します。モデルのパフォーマンスを一般化できるように十分に複雑にしつつ、トレーニング、保守、解釈が容易になるようにモデルを最適化することが、特徴選択の主なタスクです。

「機能の選択」とは、一部の機能を保持し、その他の機能を破棄できることを意味します。この記事の目的は、いくつかの機能選択戦略の概要を説明することです。

# 未使用の列を削除する
1. # 値が欠落している列を削除する
# 無関係な機能
2. 低分散特徴量
3. 多重共線性
4. 特徴係数
5. p値
6. 分散膨張係数(VIF)
7. 特徴量に基づく重要度特徴量選択
8. 自動機能選択には sci-kit learn を使用します
9. 主成分分析 (PCA)
11. このデモのデータ セットは MIT ライセンスの下にあります。 PyCaret - オープンソースのローコード機械学習ライブラリ。

データセットは非常にきれいですが、いくつかの前処理を行いました。このデータセットは、最終モデルを構築するためではなく、さまざまな特徴選択戦略がどのように機能するかを示すために使用しているため、モデルのパフォーマンスは無関係であることに注意してください。

最初にデータセットをロードします:

<span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">import</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">pandas</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">as</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">pddata</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'https://raw.githubusercontent.com/pycaret/pycaret/master/datasets/automobile.csv'</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">df</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">pd</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">read_csv</span>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">data</span>)<br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">df</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">sample</span>(<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">5</span>)

データセットには 202 行と 26 列が含まれています。各行は自動車インスタンスを表し、各列はその特性と対応するものを表します。価格。列には次のものが含まれます。

<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">df</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">columns</span><br><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">>></span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">Index</span>([<span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'symboling'</span>, <span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'normalized-losses'</span>, <span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'make'</span>, <span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'fuel-type'</span>, <span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'aspiration'</span>, <span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'num-of-doors'</span>, <span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'body-style'</span>, <span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'drive-wheels'</span>, <span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'engine-location'</span>,<span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'wheel-base'</span>, <span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'length'</span>, <span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'width'</span>, <span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'height'</span>, <span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'curb-weight'</span>, <span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'engine-type'</span>, <span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'num-of-cylinders'</span>, <span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'engine-size'</span>, <span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'fuel-system'</span>, <span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'bore'</span>, <span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'stroke'</span>, <span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'compression-ratio'</span>, <span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'horsepower'</span>, <span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'peak-rpm'</span>, <span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'city-mpg'</span>, <span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'highway-mpg'</span>, <span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'price'</span>], <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">dtype</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span><span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'object'</span>)

次に、機能選択のための 11 の戦略を詳しく見てみましょう。

1. 使用されていない列を削除する

もちろん、最も簡単な戦略は直感です。直感的ではありますが、便利な場合もありますが、一部の列は最終モデルではど​​のような形式でも使用されません (例: 「ID」、「FirstName」、「LastName」列など)。特定の列が使用されないことがわかっている場合は、自由に削除してください。私たちのデータでは、この問題が発生している列はないため、この手順では列を削除しません。

2.欠損値のある列を削除する

欠損値は機械学習では受け入れられないため、さまざまな戦略を使用して欠損データをクリーンアップします (代入など)。ただし、列に大量のデータが欠落している場合は、その列を完全に削除することをお勧めします。

<span style="color: rgb(106, 115, 125); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);"># total null values per column</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">df</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">isnull</span>().<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">sum</span>()<br><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">>></span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">symboling</span> <span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">0</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">normalized</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">-</span><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">losses</span> <span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">35</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">make</span> <span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">0</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">fuel</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">-</span><span style="color: rgb(111, 66, 193); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">type</span> <span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">0</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">aspiration</span> <span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">0</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">num</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">-</span><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">of</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">-</span><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">doors</span> <span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">2</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">body</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">-</span><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">style</span> <span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">0</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">drive</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">-</span><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">wheels</span> <span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">0</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">engine</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">-</span><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">location</span> <span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">0</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">wheel</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">-</span><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">base</span> <span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">0</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">length</span> <span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">0</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">width</span> <span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">0</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">height</span> <span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">0</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">curb</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">-</span><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">weight</span> <span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">0</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">engine</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">-</span><span style="color: rgb(111, 66, 193); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">type</span> <span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">0</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">num</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">-</span><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">of</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">-</span><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">cylinders</span> <span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">0</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">engine</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">-</span><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">size</span> <span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">0</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">fuel</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">-</span><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">system</span> <span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">0</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">bore</span> <span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">0</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">stroke</span> <span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">0</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">compression</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">-</span><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">ratio</span> <span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">0</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">horsepower</span> <span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">0</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">peak</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">-</span><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">rpm</span> <span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">0</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">city</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">-</span><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">mpg</span> <span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">0</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">highway</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">-</span><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">mpg</span> <span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">0</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">price</span> <span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">0</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">dtype</span>: <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">int64</span>

3. 無関係な特徴

アルゴリズムが回帰 (数値の予測) であっても、分類 (カテゴリーの予測) であっても、特徴はターゲットに関連している必要があります。機能に関連性が見られない場合、それは削除の主な対象となります。数値的特徴とカテゴリ的特徴の相関関係を個別にテストできます。

数値変数

<span style="color: rgb(106, 115, 125); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);"># correlation between target and features</span><br>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">df</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">corr</span>().<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">loc</span>[<span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'price'</span>].<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">plot</span>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">kind</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span><span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'barh'</span>, <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">figsize</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span>(<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">4</span>,<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">10</span>)))

##この例では、ピーク-rpm、圧縮などの機能が比率、ストローク、ボア、高さ、記号は価格とほとんど相関がないため、削除できます。

手動で列を削除することも可能ですが、相関しきい値 (この場合は 0.2) を使用してプログラムで削除することを好みます。

<span style="color: rgb(106, 115, 125); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);"># drop uncorrelated numeric features (threshold <br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">corr</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(111, 66, 193); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">abs</span>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">df</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">corr</span>().<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">loc</span>[<span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'price'</span>])<br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">corr</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">corr</span>[<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">corr</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);"><span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">0.2</span>]<br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">cols_to_drop</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">corr</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">index</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">to_list</span>()<br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">df</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">df</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">drop</span>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">cols_to_drop</span>, <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">axis</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span><span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">1</span>)</span></span>

カテゴリ変数

箱ひげ図を使用して、ターゲット特徴とカテゴリ特徴の間の相関関係を見つけることができます。

<span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">import</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">seaborn</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">as</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">sns</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">sns</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">boxplot</span>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">y</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'price'</span>, <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">x</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'fuel-type'</span>, <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">data</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">df</span>)

ディーゼル車の価格の中央値は、ディーゼル車の価格の中央値よりも高いです。ガソリン車。これは、このカテゴリ変数が自動車価格を説明するため、破棄する必要があることを意味します。このように各カテゴリ列を個別に確認することができます。

4. 低分散機能

機能の違いを確認してください:

<span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">import</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">numpy</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">as</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">np</span><br><span style="color: rgb(106, 115, 125); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);"># variance of numeric features</span><br>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">df</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">select_dtypes</span>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">include</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">np</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">number</span>).<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">var</span>().<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">astype</span>(<span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'str'</span>))

こちら「ボア」削除の候補ではありますが、分散は非常に低くなります。この特定の例では、その値が 2.54 から 3.94 の間であり、分散が低いため、これを削除することには抵抗があります:

<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">df</span>[<span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'bore'</span>].<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">describe</span>()

5 .多重共線性

多重共線性は、2 つのフィーチャ間に相関がある場合に発生します。機械学習では、各特徴が他の特徴から独立していることが期待されます。つまり、それらの間に共線性があってはなりません。高馬力車両は、エンジンサイズが大きくなる傾向があります。したがって、それらの 1 つを削除し、もう 1 つでターゲット変数である価格を決定させたい場合があります。

数値特徴とカテゴリ特徴の多重共線性を個別にテストできます。

数値変数

ヒートマップは、関連する特徴を確認して見つける最も簡単な方法です。

<span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">import</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">matplotlib</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">pyplot</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">as</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">plt</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">sns</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">set</span>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">rc</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span>{<span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'figure.figsize'</span>:(<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">16</span>,<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">10</span>)})<br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">sns</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">heatmap</span>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">df</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">corr</span>(),<br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">annot</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">True</span>,<br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">linewidths</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span><span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">.5</span>,<br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">center</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span><span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">0</span>,<br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">cbar</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">False</span>,<br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">cmap</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span><span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">"PiYG"</span>)<br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">plt</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">show</span>()

大多数特征在某种程度上相互关联，但有些特征具有非常高的相关性，例如长度与轴距以及发动机尺寸与马力。

可以根据相关阈值手动或以编程方式删除这些功能。我将手动删除具有 0.80 共线性阈值的特征。

<span style="color: rgb(106, 115, 125); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);"># drop correlated features</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">df</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">df</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">drop</span>([<span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'length'</span>, <span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'width'</span>, <span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'curb-weight'</span>, <span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'engine-size'</span>, <span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'city-mpg'</span>], <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">axis</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span><span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">1</span>)

还可以使用称为方差膨胀因子 (VIF) 的方法来确定多重共线性并根据高 VIF 值删除特征。我稍后会展示这个例子。

分类变量

与数值特征类似，也可以检查分类变量之间的共线性。诸如独立性卡方检验之类的统计检验非常适合它。

让我们检查一下数据集中的两个分类列——燃料类型和车身风格——是独立的还是相关的。

<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">df_cat</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">df</span>[[<span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'fuel-type'</span>, <span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'body-style'</span>]]<br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">df_cat</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">sample</span>(<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">5</span>)

然后我们将在每一列中创建一个类别的交叉表/列联表。

<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">crosstab</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">pd</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">crosstab</span>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">df_cat</span>[<span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'fuel-type'</span>], <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">df_cat</span>[<span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'body-style'</span>])<br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">crosstab</span>

最后，我们将在交叉表上运行卡方检验，这将告诉我们这两个特征是否独立。

<span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">from</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">scipy</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">stats</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">import</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">chi2_contingency</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">chi2_contingency</span>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">crosstab</span>)

输出依次是卡方值、p 值、自由度和预期频率数组。

p 值

由于这两个特征之间存在关联，我们可以选择删除其中一个。

到目前为止，我已经展示了在实现模型之前应用的特征选择策略。这些策略在第一轮特征选择以建立初始模型时很有用。但是一旦构建了模型，就可以获得有关模型性能中每个特征的适应度的更多信息。根据这些新信息，可以进一步确定要保留哪些功能。

下面我们使用最简单的线性模型展示其中的一些方法。

<span style="color: rgb(106, 115, 125); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);"># drop columns with missing values</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">df</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">df</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">dropna</span>()<br><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">from</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">sklearn</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">model_selection</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">import</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">train_test_split</span><br><span style="color: rgb(106, 115, 125); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);"># get dummies for categorical features</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">df</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">pd</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">get_dummies</span>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">df</span>, <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">drop_first</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">True</span>)<br><span style="color: rgb(106, 115, 125); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);"># X features</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">X</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">df</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">drop</span>(<span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'price'</span>, <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">axis</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span><span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">1</span>)<br><span style="color: rgb(106, 115, 125); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);"># y target</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">y</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">df</span>[<span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'price'</span>]<br><span style="color: rgb(106, 115, 125); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);"># split data into training and testing set</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">X_train</span>, <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">X_test</span>, <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">y_train</span>, <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">y_test</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">train_test_split</span>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">X</span>, <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">y</span>, <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">test_size</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span><span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">0.3</span>, <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">random_state</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span><span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">42</span>)<br><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">from</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">sklearn</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">linear_model</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">import</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">LinearRegression</span><br><span style="color: rgb(106, 115, 125); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);"># scaling</span><br><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">from</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">sklearn</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">preprocessing</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">import</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">StandardScaler</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">scaler</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">StandardScaler</span>()<br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">X_train</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">scaler</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">fit_transform</span>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">X_train</span>)<br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">X_test</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">scaler</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">fit_transform</span>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">X_test</span>)<br><span style="color: rgb(106, 115, 125); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);"># convert back to dataframe</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">X_train</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">pd</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">DataFrame</span>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">X_train</span>, <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">columns</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">X</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">columns</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">to_list</span>())<br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">X_test</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">pd</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">DataFrame</span>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">X_test</span>, <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">columns</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">X</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">columns</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">to_list</span>())<br><span style="color: rgb(106, 115, 125); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);"># instantiate model</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">model</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">LinearRegression</span>()<span style="color: rgb(106, 115, 125); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);"># fit</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">model</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">fit</span>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">X_train</span>, <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">y_train</span>)

现在我们已经拟合了模型，让我们进行另一轮特征选择。

6.特征系数

如果正在运行回归任务，则特征适应度的一个关键指标是回归系数（所谓的 beta 系数），它显示了模型中特征的相对贡献。有了这些信息，可以删除贡献很小或没有贡献的功能。

<span style="color: rgb(106, 115, 125); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);"># feature coefficients</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">coeffs</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">model</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">coef_</span><br><span style="color: rgb(106, 115, 125); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);"># visualizing coefficients</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">index</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">X_train</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">columns</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">tolist</span>()<br>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">pd</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">DataFrame</span>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">coeffs</span>, <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">index</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">index</span>, <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">columns</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> [<span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'coeff'</span>]).<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">sort_values</span>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">by</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'coeff'</span>)<br>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">plot</span>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">kind</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span><span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'barh'</span>, <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">figsize</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span>(<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">4</span>,<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">10</span>)))

某些特征beta 系数很小，对汽车价格的预测贡献不大。可以过滤掉这些特征：

<span style="color: rgb(106, 115, 125); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);"># filter variables near zero coefficient value</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">temp</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">pd</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">DataFrame</span>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">coeffs</span>, <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">index</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">index</span>, <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">columns</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> [<span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'coeff'</span>]).<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">sort_values</span>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">by</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'coeff'</span>)<br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">temp</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">temp</span>[(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">temp</span>[<span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'coeff'</span>]<span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">></span><span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">1</span>) <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">|</span> (<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">temp</span>[<span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'coeff'</span>]<span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);"> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">-</span><span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">1</span>)]<br><span style="color: rgb(106, 115, 125); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);"># drop those features</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">cols_coeff</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">temp</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">index</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">to_list</span>()<br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">X_train</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">X_train</span>[<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">cols_coeff</span>]<br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">X_test</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">X_test</span>[<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">cols_coeff</span>]</span>

7.p 值

在回归中，p 值告诉我们预测变量和目标之间的关系是否具有统计显著性。statsmodels 库提供了带有特征系数和相关 p 值的回归输出的函数。

如果某些特征不显著，可以将它们一个一个移除，然后每次重新运行模型，直到找到一组具有显着 p 值的特征，并通过更高的调整 R2 提高性能。

<span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">import</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">statsmodels</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">api</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">as</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">sm</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">ols</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">sm</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">OLS</span>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">y</span>, <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">X</span>).<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">fit</span>()<br><span style="color: rgb(111, 66, 193); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">print</span>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">ols</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">summary</span>())

8.方差膨胀因子 (VIF)

方差膨胀因子 (VIF) 是衡量多重共线性的另一种方法。它被测量为整体模型方差与每个独立特征的方差的比率。一个特征的高 VIF 表明它与一个或多个其他特征相关。根据经验：

• VIF = 1 表示无相关性
• VIF = 1-5 中等相关性
• VIF >5 高相关

VIF 是一种消除多重共线性特征的有用技术。对于我们的演示，将所有 VIF 高于10的删除。

<span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">from</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">statsmodels</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">stats</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">outliers_influence</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">import</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">variance_inflation_factor</span><br><span style="color: rgb(106, 115, 125); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);"># calculate VIF</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">vif</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">pd</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">Series</span>([<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">variance_inflation_factor</span>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">X</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">values</span>, <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">i</span>) <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">for</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">i</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">in</span> <span style="color: rgb(111, 66, 193); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">range</span>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">X</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">shape</span>[<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">1</span>])], <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">index</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">X</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">columns</span>)<br><span style="color: rgb(106, 115, 125); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);"># display VIFs in a table</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">index</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">X_train</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">columns</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">tolist</span>()<br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">vif_df</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">pd</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">DataFrame</span>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">vif</span>, <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">index</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">index</span>, <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">columns</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> [<span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'vif'</span>]).<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">sort_values</span>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">by</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'vif'</span>, <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">ascending</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">False</span>)<br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">vif_df</span>[<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">vif_df</span>[<span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'vif'</span>]<span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);"><span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">10</span>]</span>

9.基于特征重要性选择

决策树/随机森林使用一个特征来分割数据，该特征最大程度地减少了杂质(以基尼系数杂质或信息增益衡量)。找到最佳特征是算法如何在分类任务中工作的关键部分。我们可以通过 feature_importances_ 属性访问最好的特征。

让我们在我们的数据集上实现一个随机森林模型并过滤一些特征。

<span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">from</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">sklearn</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">ensemble</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">import</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">RandomForestClassifier</span><br><span style="color: rgb(106, 115, 125); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);"># instantiate model</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">model</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">RandomForestClassifier</span>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">n_estimators</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span><span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">200</span>, <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">random_state</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span><span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">0</span>)<br><span style="color: rgb(106, 115, 125); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);"># fit model</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">model</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">fit</span>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">X</span>,<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">y</span>)

现在让我们看看特征重要性：

<span style="color: rgb(106, 115, 125); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);"># feature importance</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">importances</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">model</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">feature_importances_</span><br><span style="color: rgb(106, 115, 125); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);"># visualization</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">cols</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">X</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">columns</span><br>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">pd</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">DataFrame</span>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">importances</span>, <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">cols</span>, <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">columns</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> [<span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'importance'</span>])<br>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">sort_values</span>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">by</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span><span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'importance'</span>, <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">ascending</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">True</span>)<br>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">plot</span>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">kind</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span><span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'barh'</span>, <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">figsize</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span>(<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">4</span>,<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">10</span>)))

上面的输出显示了每个特征在减少每个节点/拆分处的重要性。

由于随机森林分类器有很多估计量（例如上面例子中的 200 棵决策树），可以用置信区间计算相对重要性的估计值。

<span style="color: rgb(106, 115, 125); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);"># calculate standard deviation of feature importances</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">std</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">np</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">std</span>([<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">i</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">feature_importances_</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">for</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">i</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">in</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">model</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">estimators_</span>], <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">axis</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span><span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">0</span>)<br><span style="color: rgb(106, 115, 125); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);"># visualization</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">feat_with_importance</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">pd</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">Series</span>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">importances</span>, <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">X</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">columns</span>)<br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">fig</span>, <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">ax</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">plt</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">subplots</span>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">figsize</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span>(<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">12</span>,<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">5</span>))<br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">feat_with_importance</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">plot</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">bar</span>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">yerr</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">std</span>, <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">ax</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">ax</span>)<br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">ax</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">set_title</span>(<span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">"Feature importances"</span>)<br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">ax</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">set_ylabel</span>(<span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">"Mean decrease in impurity"</span>)

现在我们知道了每个特征的重要性，可以手动（或以编程方式）确定保留哪些特征以及删除哪些特征。

10.使用 Scikit Learn 自动选择特征

sklearn 库中有一个完整的模块，只需几行代码即可处理特征选择。

sklearn 中有许多自动化流程，但这里我只展示一些：

<span style="color: rgb(106, 115, 125); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);"># import modules</span><br><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">from</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">sklearn</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">feature_selection</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">import</span> (<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">SelectKBest</span>, <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">chi2</span>, <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">SelectPercentile</span>, <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">SelectFromModel</span>, <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">SequentialFeatureSelector</span>, <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">SequentialFeatureSelector</span>)

基于卡方的技术

基于卡方的技术根据一些预定义的分数选择特定数量的用户定义特征 (k)。这些分数是通过计算 X（独立）和 y（因）变量之间的卡方统计量来确定的。在 sklearn 中，需要做的就是确定要保留多少特征。如果想保留 10 个功能，实现将如下所示：

<span style="color: rgb(106, 115, 125); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);"># select K best features</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">X_best</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">SelectKBest</span>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">chi2</span>, <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">k</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span><span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">10</span>).<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">fit_transform</span>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">X</span>,<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">y</span>)<br><span style="color: rgb(106, 115, 125); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);"># number of best features</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">X_best</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">shape</span>[<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">1</span>]<br><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">>></span> <span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">10</span>

如果有大量特征，可以指定要保留的特征百分比。假设我们想要保留 75% 的特征并丢弃剩余的 25%：

<span style="color: rgb(106, 115, 125); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);"># keep 75% top features</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">X_top</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">SelectPercentile</span>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">chi2</span>, <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">percentile</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">75</span>).<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">fit_transform</span>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">X</span>,<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">y</span>)<br><span style="color: rgb(106, 115, 125); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);"># number of best features</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">X_top</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">shape</span>[<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">1</span>]<br><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">>></span> <span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">36</span>

正则化

正则化减少了过拟合。如果你有太多的特征，正则化控制它们的效果，或者通过缩小特征系数（称为 L2 正则化）或将一些特征系数设置为零（称为 L1 正则化）。

一些模型具有内置的 L1/L2 正则化作为超参数来惩罚特征。可以使用转换器 SelectFromModel 消除这些功能。

让我们实现一个带有惩罚 = 'l1' 的 LinearSVC 算法。然后使用 SelectFromModel 删除一些功能。

<span style="color: rgb(106, 115, 125); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);"># implement algorithm</span><br><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">from</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">sklearn</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">svm</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">import</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">LinearSVC</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">model</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">LinearSVC</span>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">penalty</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'l1'</span>, <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">C</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">0.002</span>, <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">dual</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">False</span>)<br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">model</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">fit</span>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">X</span>,<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">y</span>)<br><span style="color: rgb(106, 115, 125); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);"># select features using the meta transformer</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">selector</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">SelectFromModel</span>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">estimator</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">model</span>, <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">prefit</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">True</span>)<br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">X_new</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">selector</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">transform</span>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">X</span>)<br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">X_new</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">shape</span>[<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">1</span>]<br><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">>></span> <span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">2</span><br><span style="color: rgb(106, 115, 125); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);"># names of selected features</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">feature_names</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">np</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">array</span>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">X</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">columns</span>)<br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">feature_names</span>[<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">selector</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">get_support</span>()]<br><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">>></span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">array</span>([<span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'wheel-base'</span>, <span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'horsepower'</span>], <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">dtype</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span><span style="color: rgb(111, 66, 193); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">object</span>)

序贯法

序贯法是一种经典的统计技术。在这种情况下一次添加/删除一个功能并检查模型性能，直到它针对需求进行优化。

序贯法有两种变体。前向选择技术从 0 特征开始，然后添加一个最大程度地减少错误的特征；然后添加另一个特征，依此类推。

向后选择在相反的方向上起作用。模型从包含的所有特征开始并计算误差；然后它消除了一个可以进一步减少误差的特征。重复该过程，直到保留所需数量的特征。

<span style="color: rgb(106, 115, 125); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);"># instantiate model</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">model</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">RandomForestClassifier</span>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">n_estimators</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span><span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">100</span>, <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">random_state</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span><span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">0</span>)<br><span style="color: rgb(106, 115, 125); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);"># select features</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">selector</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">SequentialFeatureSelector</span>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">estimator</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">model</span>, <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">n_features_to_select</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span><span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">10</span>, <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">direction</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span><span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'backward'</span>, <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">cv</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span><span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">2</span>)<br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">selector</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">fit_transform</span>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">X</span>,<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">y</span>)<br><span style="color: rgb(106, 115, 125); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);"># check names of features selected</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">feature_names</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">np</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">array</span>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">X</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">columns</span>)<br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">feature_names</span>[<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">selector</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">get_support</span>()]<br><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">>></span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">array</span>([<span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'bore'</span>, <span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'make_mitsubishi'</span>, <span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'make_nissan'</span>, <span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'make_saab'</span>,<br><span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'aspiration_turbo'</span>, <span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'num-of-doors_two'</span>, <span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'body style_hatchback'</span>, <span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'engine-type_ohc'</span>, <span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'num-of-cylinders_twelve'</span>, <span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">'fuel-system_spdi'</span>], <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">dtype</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span><span style="color: rgb(111, 66, 193); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">object</span>)

11.主成分分析 (PCA)

PCA的主要目的是降低高维特征空间的维数。原始特征被重新投影到新的维度（即主成分）。最终目标是找到最能解释数据方差的特征数量。

<span style="color: rgb(106, 115, 125); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);"># import PCA module</span><br><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">from</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">sklearn</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">decomposition</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">import</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">PCA</span><br><span style="color: rgb(106, 115, 125); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);"># scaling data</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">X_scaled</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">scaler</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">fit_transform</span>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">X</span>)<br><span style="color: rgb(106, 115, 125); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);"># fit PCA to data</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">pca</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">PCA</span>()<br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">pca</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">fit</span>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">X_scaled</span>)<br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">evr</span> <span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span> <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">pca</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">explained_variance_ratio_</span><br><span style="color: rgb(106, 115, 125); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);"># visualizing the variance explained by each principal components</span><br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">plt</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">figure</span>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">figsize</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span>(<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">12</span>, <span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">5</span>))<br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">plt</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">plot</span>(<span style="color: rgb(111, 66, 193); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">range</span>(<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">0</span>, <span style="color: rgb(111, 66, 193); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">len</span>(<span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">evr</span>)), <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">evr</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">cumsum</span>(), <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">marker</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span><span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">"o"</span>, <span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">linestyle</span><span style="color: rgb(215, 58, 73); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">=</span><span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">"--"</span>)<br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">plt</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">xlabel</span>(<span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">"Number of components"</span>)<br><span style="color: rgb(89, 89, 89); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">plt</span>.<span style="color: rgb(0, 92, 197); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">ylabel</span>(<span style="color: rgb(102, 153, 0); margin: 0px; padding: 0px; background: none 0% 0% / auto repeat scroll padding-box border-box rgba(0, 0, 0, 0);">"Cumulative explained variance"</span>)

20 个主成分解释了超过 80% 的方差，因此可以将模型拟合到这 20 个成分（特征）。可以预先确定方差阈值并选择所需的主成分数量。

总结

这是对可应用于特征选择的各种技术的有用指南。在拟合模型之前应用了一些技术，例如删除具有缺失值的列、不相关的列、具有多重共线性的列以及使用 PCA 进行降维，而在基本模型实现之后应用其他技术，例如特征系数、p 值、 VIF 等。虽然不会在一个项目中完全使用所有策略，这些策略都是我们进行测试的方向。

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