Softmax regression

import tensorflow as tf
from tensorflow.examples.tutorials.mnist import input_data

mnist = input_data.read_data_sets("MNIST_data/", one_hot=True)

x = tf.placeholder(tf.float32, [None, 784])
W = tf.Variable(tf.zeros([784, 10]))
b = tf.Variable(tf.zeros([10]))

y = tf.nn.softmax(tf.matmul(x, W) + b)
y_ = tf.placeholder(tf.float32, [None, 10])

# loss func
cross_entropy = -tf.reduce_sum(y_ * tf.log(y))
train_step = tf.train.GradientDescentOptimizer(0.01).minimize(cross_entropy)

with tf.Session() as sess:
    tf.initialize_all_variables().run()

    # train
    for i in range(1000):
        batch_xs, batch_ys = mnist.train.next_batch(100)
        sess.run(train_step, feed_dict={x: batch_xs, y_: batch_ys})
    
    correct_prediction = tf.equal(tf.arg_max(y, 1), tf.arg_max(y_, 1))
    accuracy = tf.reduce_mean(tf.cast(correct_prediction, "float"))
    print("Accuarcy on Test-dataset: ", sess.run(accuracy, feed_dict={x: mnist.test.images, y_: mnist.test.labels}))
('Accuarcy on Test-dataset: ', 0.91140002)

Softmax

%matplotlib inline
"""Softmax."""

scores = np.array([3.0, 1.0, 0.2])

import numpy as np

def softmax(x):
    """Compute softmax values for each sets of scores in x."""
    return np.exp(x)/np.sum(np.exp(x), axis=0)

# print(softmax(scores*10)) -> classifier become very confident about its predictions
# print(softmax(scores/10)) -> classifier become very unsure
print(softmax(scores))

# Plot softmax curves
import matplotlib.pyplot as plt
x = np.arange(-2.0, 6.0, 0.1)
scores = np.vstack([x, np.ones_like(x), 0.2 * np.ones_like(x)])

plt.plot(x, softmax(scores).T, linewidth=2)
plt.show()
[ 0.8360188   0.11314284  0.05083836]

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