用TensorFlow实现弹性网络回归算法

弹性网络回归算法（Elastic Net Regression）是综合lasso回归和岭回归的一种回归算法，通过在损失函数中增加L1和L2正则项。

本文使用多线性回归的方法实现弹性网络回归算法，以iris数据集为训练数据，用花瓣长度、花瓣宽度和花萼宽度三个特征预测花萼长度。

# Elastic Net Regression
# 弹性网络回归
#----------------------------------
#
# This function shows how to use TensorFlow to
# solve elastic net regression.
# y = Ax + b
#
# We will use the iris data, specifically:
#  y = Sepal Length
#  x = Pedal Length, Petal Width, Sepal Width

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

###
# Set up for TensorFlow
###

ops.reset_default_graph()

# Create graph
sess = tf.Session()

###
# Obtain data
###

# Load the data
# iris.data = [(Sepal Length, Sepal Width, Petal Length, Petal Width)]
iris = datasets.load_iris()
x_vals = np.array([[x[1], x[2], x[3]] for x in iris.data])
y_vals = np.array([y[0] for y in iris.data])

###
# Setup model
###

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

# Declare batch size
batch_size = 50

# Initialize placeholders
x_data = tf.placeholder(shape=[None, 3], dtype=tf.float32)
y_target = tf.placeholder(shape=[None, 1], dtype=tf.float32)

# Create variables for linear regression
A = tf.Variable(tf.random_normal(shape=[3,1]))
b = tf.Variable(tf.random_normal(shape=[1,1]))

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

# Declare the elastic net loss function
# 对于弹性网络回归算法，损失函数包含斜率的L1正则和L2正则。
# 创建L1和L2正则项，然后加入到损失函数中
elastic_param1 = tf.constant(1.)
elastic_param2 = tf.constant(1.)
l1_a_loss = tf.reduce_mean(tf.abs(A))
l2_a_loss = tf.reduce_mean(tf.square(A))
e1_term = tf.multiply(elastic_param1, l1_a_loss)
e2_term = tf.multiply(elastic_param2, l2_a_loss)
loss = tf.expand_dims(tf.add(tf.add(tf.reduce_mean(tf.square(y_target - model_output)), e1_term), e2_term), 0)

# Declare optimizer
my_opt = tf.train.GradientDescentOptimizer(0.0001)
train_step = my_opt.minimize(loss)

###
# Train model
###

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

# Training loop
loss_vec = []
for i in range(1000):
    rand_index = np.random.choice(len(x_vals), size=batch_size)
    rand_x = 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)%250==0:
        print('Step #' + str(i+1) + ' A = ' + str(sess.run(A)) + ' b = ' + str(sess.run(b)))
        print('Loss = ' + str(temp_loss))

###
# Extract model results
###

# Get the optimal coefficients
[[sw_coef], [pl_coef], [pw_ceof]] = sess.run(A)
[y_intercept] = sess.run(b)

###
# Plot results
###

# Plot loss over time
plt.plot(loss_vec, 'k-')
plt.title('Loss per Generation')
plt.xlabel('Generation')
plt.ylabel('Loss')
plt.show()

结果：

Step #250 A = [[ 0.93870646]
 [-0.37139279]
 [ 0.27290201]] b = [[-0.36246276]]
Loss = [ 23.83867645]
Step #500 A = [[ 1.26683569]
 [ 0.14753909]
 [ 0.42754883]] b = [[-0.2424359]]
Loss = [ 2.98364353]
Step #750 A = [[ 1.33217096]
 [ 0.28339788]
 [ 0.45837855]] b = [[-0.20850581]]
Loss = [ 1.82120061]
Step #1000 A = [[ 1.33412337]
 [ 0.32563502]
 [ 0.45811999]] b = [[-0.19569117]]
Loss = [ 1.64923525]