tensorflow 损失函数

#**********************回归损失

import matplotlib.pyplot as plt

import tensorflow as tf

from tensorflow.python.framework import ops

ops.reset_default_graph()

 

sess = tf.Session()

 

# Various Predicted X-values

x_vals = tf.linspace(-1., 1., 500)

# Create our target of zero

target = tf.constant(0.)

 

# L2正则损失函数

#即欧拉损失函数。L2正则损失函数是预测值与目标值差值的平方和。L2正则损失函数是非常有用的损失函数，因为它在目标值附近有更好的曲度，机器学习算法利用这点收敛，并且离目标越近收敛越慢。

# L2 loss

# L = (pred - actual)^2

l2_y_vals = tf.square(target - x_vals)

l2_y_out = sess.run(l2_y_vals)

 

#即绝对值损失函数。与L2正则损失函数对差值求平方不同的是，L1正则损失函数对差值求绝对值。L1正则在目标值附近不平滑，这会导致算法不能很好地收敛。

# L1 loss

# L = abs(pred - actual)

l1_y_vals = tf.abs(target - x_vals)

l1_y_out = sess.run(l1_y_vals)

 

#Pseudo-Huber损失函数是Huber损失函数的连续、平滑估计，试图利用L1和L2正则削减极值处的陡峭，使得目标值附近连续。它的表达式以来参数delta。

#L = delta^2 * (sqrt(1 + ((pred - actual)/delta)^2) - 1)

 

# Pseudo-Huber with delta = 0.25

delta1 = tf.constant(0.25)

phuber1_y_vals = tf.multiply(tf.square(delta1), tf.sqrt(1. + tf.square((target - x_vals)/delta1)) - 1.)

phuber1_y_out = sess.run(phuber1_y_vals)

 

# Pseudo-Huber with delta = 5

delta2 = tf.constant(5.)

phuber2_y_vals = tf.multiply(tf.square(delta2), tf.sqrt(1. + tf.square((target - x_vals)/delta2)) - 1.)

phuber2_y_out = sess.run(phuber2_y_vals)

 

 

x_array = sess.run(x_vals)

plt.plot(x_array, l2_y_out, 'b-', label='L2 Loss')

plt.plot(x_array, l1_y_out, 'r--', label='L1 Loss')

plt.plot(x_array, phuber1_y_out, 'k-.', label='P-Huber Loss (0.25)')

plt.plot(x_array, phuber2_y_out, 'g:', label='P-Huber Loss (5.0)')

plt.ylim(-0.2, 0.4)

plt.legend(loc='lower right', prop={'size': 11})

plt.grid()

plt.show()

 

 

 

# Various predicted X values

x_vals = tf.linspace(-3., 5., 500)

 

# Target of 1.0

target = tf.constant(1.)

targets = tf.fill([500,], 1.)

 

# Hinge损失函数主要用来评估支持向量机算法，但有时也用来评估神经网络算法。

# Use for predicting binary (-1, 1) classes

# L = max(0, 1 - (pred * actual))

hinge_y_vals = tf.maximum(0., 1. - tf.multiply(target, x_vals))

hinge_y_out = sess.run(hinge_y_vals)

 

# Cross entropy loss

# L = -actual * (log(pred)) - (1-actual)(log(1-pred))

xentropy_y_vals = - tf.multiply(target, tf.log(x_vals)) - tf.multiply((1. - target), tf.log(1. - x_vals))

xentropy_y_out = sess.run(xentropy_y_vals)

 

# L = -actual * (log(sigmoid(pred))) - (1-actual)(log(1-sigmoid(pred)))

# or

# L = max(actual, 0) - actual * pred + log(1 + exp(-abs(actual)))

x_val_input = tf.expand_dims(x_vals, 1)

target_input = tf.expand_dims(targets, 1)

xentropy_sigmoid_y_vals = tf.nn.sigmoid_cross_entropy_with_logits(logits=x_val_input, labels=target_input)

xentropy_sigmoid_y_out = sess.run(xentropy_sigmoid_y_vals)

 

# Weighted cross entropy loss

# L = -actual * (log(pred)) * weights - (1-actual)(log(1-pred))

# or

# L = (1 - pred) * actual + (1 + (weights - 1) * pred) * log(1 + exp(-actual))

weight = tf.constant(0.5)

xentropy_weighted_y_vals = tf.nn.weighted_cross_entropy_with_logits(logits=x_vals, targets=targets, pos_weight=weight)

xentropy_weighted_y_out = sess.run(xentropy_weighted_y_vals)

 

 

# Plot the output

x_array = sess.run(x_vals)

plt.plot(x_array, hinge_y_out, 'b-', label='Hinge Loss')

plt.plot(x_array, xentropy_y_out, 'r--', label='Cross Entropy Loss')

plt.plot(x_array, xentropy_sigmoid_y_out, 'k-.', label='Cross Entropy Sigmoid Loss')

plt.plot(x_array, xentropy_weighted_y_out, 'g:', label='Weighted Cross Entropy Loss (x0.5)')

plt.ylim(-1.5, 3)

plt.legend(loc='lower right', prop={'size': 11})

plt.grid()

plt.show()