用TensorFlow实现lasso回归和岭回归算法的示例

# 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 'Ridge' or 'LASSO'

regression_type = 'LASSO'

# 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 == 'LASSO':

  # 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 == 'Ridge':

  # 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('Invalid regression_type parameter value',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('Step #' + str(i+1) + ' A = ' + str(sess.run(A)) + ' b = ' + str(sess.run(b)))

    print('Loss = ' + str(temp_loss))

    print('\n')

###

# 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, 'o', label='Data Points')

plt.plot(x_vals, best_fit, 'r-', label='Best fit line', linewidth=3)

plt.legend(loc='upper left')

plt.title('Sepal Length vs Pedal Width')

plt.xlabel('Pedal Width')

plt.ylabel('Sepal Length')

plt.show()

# Plot loss over time

plt.plot(loss_vec, 'k-')

plt.title(regression_type + ' Loss per Generation')

plt.xlabel('Generation')

plt.ylabel('Loss')

plt.show()