用TensorFlow實作lasso迴歸和嶺迴歸演算法的範例-Python教學-PHP中文網

這篇文章主要介紹了關於用TensorFlow實現lasso回歸和嶺回歸演算法的範例，有著一定的參考價值，現在分享給大家，有需要的朋友可以參考一下

也有些正規方法可以限制迴歸演算法輸出結果中係數的影響，其中最常用的兩種正規方法是lasso迴歸和嶺迴歸。

lasso迴歸和嶺迴歸演算法跟常規線性迴歸演算法極為相似，有一點不同的是，在公式中增加正規項來限制斜率（或淨斜率）。這樣做的主要原因是限制特徵對因變數的影響，透過增加一個依賴斜率A的損失函數來實現。

對於lasso迴歸演算法，在損失函數上增加一項：斜率A的某個給定倍數。我們使用TensorFlow的邏輯操作，但沒有這些操作相關的梯度，而是使用階躍函數的連續估計，也稱為連續階躍函數，其會在截止點跳躍擴大。一會兒就可以看到如何使用lasso迴歸演算法。

對於嶺迴歸演算法，增加一個L2範數，即斜率係數的L2正則。

# LASSO and Ridge Regression
# lasso回归和岭回归
# 
# This function shows how to use TensorFlow to solve LASSO or 
# Ridge regression for 
# y = Ax + b
# 
# We will use the iris data, specifically: 
#  y = Sepal Length 
#  x = Petal Width

# import required libraries
import matplotlib.pyplot as plt
import sys
import numpy as np
import tensorflow as tf
from sklearn import datasets
from tensorflow.python.framework import ops


# Specify &#39;Ridge&#39; or &#39;LASSO&#39;
regression_type = &#39;LASSO&#39;

# clear out old graph
ops.reset_default_graph()

# Create graph
sess = tf.Session()

###
# Load iris data
###

# iris.data = [(Sepal Length, Sepal Width, Petal Length, Petal Width)]
iris = datasets.load_iris()
x_vals = np.array([x[3] for x in iris.data])
y_vals = np.array([y[0] for y in iris.data])

###
# Model Parameters
###

# Declare batch size
batch_size = 50

# Initialize placeholders
x_data = tf.placeholder(shape=[None, 1], dtype=tf.float32)
y_target = tf.placeholder(shape=[None, 1], dtype=tf.float32)

# make results reproducible
seed = 13
np.random.seed(seed)
tf.set_random_seed(seed)

# Create variables for linear regression
A = tf.Variable(tf.random_normal(shape=[1,1]))
b = tf.Variable(tf.random_normal(shape=[1,1]))

# Declare model operations
model_output = tf.add(tf.matmul(x_data, A), b)

###
# Loss Functions
###

# Select appropriate loss function based on regression type

if regression_type == &#39;LASSO&#39;:
  # Declare Lasso loss function
  # 增加损失函数，其为改良过的连续阶跃函数，lasso回归的截止点设为0.9。
  # 这意味着限制斜率系数不超过0.9
  # Lasso Loss = L2_Loss + heavyside_step,
  # Where heavyside_step ~ 0 if A < constant, otherwise ~ 99
  lasso_param = tf.constant(0.9)
  heavyside_step = tf.truep(1., tf.add(1., tf.exp(tf.multiply(-50., tf.subtract(A, lasso_param)))))
  regularization_param = tf.multiply(heavyside_step, 99.)
  loss = tf.add(tf.reduce_mean(tf.square(y_target - model_output)), regularization_param)

elif regression_type == &#39;Ridge&#39;:
  # Declare the Ridge loss function
  # Ridge loss = L2_loss + L2 norm of slope
  ridge_param = tf.constant(1.)
  ridge_loss = tf.reduce_mean(tf.square(A))
  loss = tf.expand_dims(tf.add(tf.reduce_mean(tf.square(y_target - model_output)), tf.multiply(ridge_param, ridge_loss)), 0)

else:
  print(&#39;Invalid regression_type parameter value&#39;,file=sys.stderr)


###
# Optimizer
###

# Declare optimizer
my_opt = tf.train.GradientDescentOptimizer(0.001)
train_step = my_opt.minimize(loss)

###
# Run regression
###

# Initialize variables
init = tf.global_variables_initializer()
sess.run(init)

# Training loop
loss_vec = []
for i in range(1500):
  rand_index = np.random.choice(len(x_vals), size=batch_size)
  rand_x = np.transpose([x_vals[rand_index]])
  rand_y = np.transpose([y_vals[rand_index]])
  sess.run(train_step, feed_dict={x_data: rand_x, y_target: rand_y})
  temp_loss = sess.run(loss, feed_dict={x_data: rand_x, y_target: rand_y})
  loss_vec.append(temp_loss[0])
  if (i+1)%300==0:
    print(&#39;Step #&#39; + str(i+1) + &#39; A = &#39; + str(sess.run(A)) + &#39; b = &#39; + str(sess.run(b)))
    print(&#39;Loss = &#39; + str(temp_loss))
    print(&#39;\n&#39;)

###
# Extract regression results
###

# Get the optimal coefficients
[slope] = sess.run(A)
[y_intercept] = sess.run(b)

# Get best fit line
best_fit = []
for i in x_vals:
 best_fit.append(slope*i+y_intercept)


###
# Plot results
###

# Plot regression line against data points
plt.plot(x_vals, y_vals, &#39;o&#39;, label=&#39;Data Points&#39;)
plt.plot(x_vals, best_fit, &#39;r-&#39;, label=&#39;Best fit line&#39;, linewidth=3)
plt.legend(loc=&#39;upper left&#39;)
plt.title(&#39;Sepal Length vs Pedal Width&#39;)
plt.xlabel(&#39;Pedal Width&#39;)
plt.ylabel(&#39;Sepal Length&#39;)
plt.show()

# Plot loss over time
plt.plot(loss_vec, &#39;k-&#39;)
plt.title(regression_type + &#39; Loss per Generation&#39;)
plt.xlabel(&#39;Generation&#39;)
plt.ylabel(&#39;Loss&#39;)
plt.show()

登入後複製

輸出結果：

Step #300 A = [[ 0.77170753]] b = [[ 1.82499862]]
Loss = [[ 10.26473045]]
Step #600 A = [[ 0.75908542]] b = [[ 3.2220633]]
Loss = [[ 3.06292033]]##Step #007485. ] b = [[ 3.9975822]]
Loss = [[ 1.23220456]]
Step #1200 A = [[ 0.73752165]] b = [[ 4.42974091]]##Loss5 = [ ] b = [[ 4.42974091]]##Loss5 = [ 0.57]#7057]#。 #Step #1500 A = [[ 0.72942668]] b = [[ 4.67253113]]
Loss = [[ 0.40874988]]

透過在標準線性迴歸估計的基礎上，增加一個連續的階躍函數，實現lasso迴歸演算法。由於階躍函數的坡度，我們需要注意步長，因為太大的步長會導致最終不收斂。