Must-know data science: 10 important concepts + the meaning of 22 charts

01 Bias-variance trade-off

This is a concept that always ranks at the top of the most important theories of machine learning. Almost all algorithms in machine learning (including deep learning) strive to strike the right balance between bias and variance, and this diagram clearly explains the opposition between the two.

02 Gini Impurity and Entropy

Gini (a measure of lack of homogeneity) and Entropy (a measure of randomness) are both decisions A measure of the impurity of nodes in a tree.

For these two concepts it is more important to understand the relationship between them in order to be able to use Choose the right indicator for the scenario.

Gini impurity (coefficient) is generally easier to calculate than entropy (because entropy involves logarithmic calculations).

03 Precision and Recall Curve

The precision-recall curve shows the trade-off between precision and recall for different thresholds. A large area under the curve represents high recall and high precision, where high precision is related to low false alarm rates, and high recall is related to low false alarm rates.

It can help us choose the right threshold according to our needs. For example, if our goal is to reduce type 1 error, we need to choose high precision, whereas if our goal is to minimize type 2 error, then we should choose a threshold such that the recall is high.

• #The accuracy denominator is a variable: i.e. false positives (negative samples classified as positive) will change every time.
• The recall denominator is a constant: it represents the total number of true values ​​and therefore will always remain the same.

This is why the graph below shows Precision having a wave at the end, while Recall always remains flat.

04 ROC Curve

The ROC curve is a graph that shows the performance of a classification model at all classification thresholds.

This curve plots two parameters:

真阳性率<br>误报率

The area under this curve (called AUC) can also be used as a performance metric. The higher the AUC, the better the model.

05 弯头曲线

用于K-means算法中最优簇数的选择。WCSS（簇内平方和）是给定簇中每个点与质心之间的平方距离之和。当我们用 K（簇数）值绘制 WCSS 时，该图看起来像一个肘部（弯头）。

随着聚类数量的增加，WCSS 值将开始下降。K = 1时WCSS值最大

06三块地块

它帮助我们在对高维数据执行主成分分析后，可视化每个主成分解释的变异百分比。为了选择正确数量的主成分来考虑我们的模型，我们通常会绘制此图并选择能够为我们提供足够好的总体方差百分比的值。

07线性和逻辑回归曲线

对于线性可分数据，我们可以进行线性回归或逻辑回归，二者都可以作为决策边界曲线/线。但是，在逻辑回归的情况下，由于通常只有 2 个类别，因此具有线性直线决策边界可能不起作用，在一条直线上值从低到高非常均匀地上升，因为它不够陡峭在值突然上升后会得到很多临界的高值或者低值，最终会错误分类。因此，"边界"区域，即概率从高到低转变的区域并不真正存在。所以一般情况下会应用 sigmoid 变换将其转换为 sigmoid 曲线，该曲线在极端情况下是平滑的，在中间几乎是线性的。

08支持向量机（几何理解）

09标准正态分布规则（z-分布）

均值为0，标准差为1的特殊正态分布。

经验法则指出，按照正态分布观察到的数据中有 99.7% 位于平均值的 3 个标准差以内。根据该规则，68% 的数据在一个标准差内，95% 在两个标准差内，99.7% 在三个标准差内。10学生T分布T 分布（也称为学生 T 分布）是一系列分布，看起来几乎与正态分布曲线相同，只是更短和更宽/更胖。当我们有较小的样本时，我们使用 T分布而不是正态分布。样本量越大，t 分布越像正态分布。事实上，在 30 个样本之后，T 分布几乎与正态分布完全一样。

Summary

We may come across many small but critical concepts that form the basis for us to make a decision or choose the right model. The important concepts mentioned in this article can be represented by related diagrams. These concepts are very important and we need to know their meaning the first time we see them. If you have mastered the above concepts, Then you can try to explain what the following picture represents:

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