回归算法、分类算法的损失函数的图示

import matplotlib.pyplot as plt
import tensorflow as tf

sess = tf.Session()
x_vals = tf.linspace(-1., 1., 500)
target = tf.constant(0.)

l2_y_vals = tf.square(target - x_vals)
l2_y_out = sess.run(l2_y_vals)

l1_y_vals = tf.abs(target - x_vals)
l1_y_out = sess.run(l1_y_vals)

delta1 = tf.constant(0.25)
phuber1_y_als = tf.multiply(tf.square(delta1), tf.sqrt(1. + tf.square((target - x_vals) / delta1)) - 1.)
phuber1_y_out = sess.run(phuber1_y_als)

delta2 = tf.constant(5.)
phuber2_y_als = tf.multiply(tf.square(delta2), tf.sqrt(1. + tf.square((target - x_vals) / delta2)) - 1.)
phuber2_y_out = sess.run(phuber2_y_als)

# 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.show()

x_vals = tf.linspace(-3., 5., 500)
target = tf.constant(1.)
targets = tf.fill([500, ], 1.)

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

# [i for i  in xentropy_y_out if not sess.run(tf.is_nan(i))]
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)
not_nan = [i for i in xentropy_y_out if not sess.run(tf.is_nan(i))]

# logits and targets must have the same type and shape.
# ValueError: Only call `sigmoid_cross_entropy_with_logits` with named arguments (labels=..., logits=..., ...)
xentropy_sigmoid_y_vals = tf.nn.sigmoid_cross_entropy_with_logits(labels=x_vals, logits=targets)
xentropy_sigmoid_y_out = sess.run(xentropy_sigmoid_y_vals)

weight = tf.constant(0.5)
xentropy_weigthed_y_vals = tf.nn.weighted_cross_entropy_with_logits(x_vals, targets, weight)
xentropy_weigthed_y_out = sess.run(xentropy_weigthed_y_vals)

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_weigthed_y_out, 'g:', label='Weighted Cross Entropy Sigmoid Loss (*0.5)')
plt.ylim(-1.5, 3)
plt.legend(loc='lower right', prop={'size': 11})
plt.show()

# unscaled_logits = tf.constant([1., -3., 10.])
# target_dist = tf.constant([0.1, 0.02, 0.88])
# softmax_xentropy = tf.nn.softmax_cross_entropy_with_logits_v2(labels=unscaled_logits, logits=target_dist)
# print(sess.run(softmax_xentropy))
# softmax_xentropy_out = sess.run(softmax_xentropy)
#
# unscaled_logits = tf.constant([1., -3., 10.])
# sparse_target_dist = tf.constant([2])
# sparse_xentropy = tf.nn.sparse_softmax_cross_entropy_with_logits(labels=unscaled_logits, logits=sparse_target_dist)
# print(sess.run(sparse_xentropy))
# sparse_xentropy_out = sess.run(sparse_xentropy)
dd = 9