Logistic Regression in TensorFlow¶
Credits: Forked from TensorFlow-Examples by Aymeric Damien
Logistic regression is the simplest classification model and serves as the building block of neural networks – each neuron in a network is essentially a logistic regression unit. Here we classify handwritten digits from the MNIST dataset (28x28 pixel grayscale images flattened to 784-dimensional vectors) into 10 classes (digits 0-9).
The model computes softmax(X * W + b) where softmax converts raw scores into probabilities that sum to 1. The loss function is cross-entropy, which measures the distance between the predicted probability distribution and the true one-hot label. Training uses mini-batch gradient descent (batches of 100 samples), which is faster and more stable than processing one sample at a time. This exact pattern – forward pass, loss computation, backward pass, parameter update – is the core loop of all deep learning training.
Setup: Refer to the setup instructions
# Import MINST data
import input_data
mnist = input_data.read_data_sets("/tmp/data/", one_hot=True)
import tensorflow as tf
# Parameters
learning_rate = 0.01
training_epochs = 25
batch_size = 100
display_step = 1
# tf Graph Input
x = tf.placeholder("float", [None, 784]) # mnist data image of shape 28*28=784
y = tf.placeholder("float", [None, 10]) # 0-9 digits recognition => 10 classes
# Create model
# Set model weights
W = tf.Variable(tf.zeros([784, 10]))
b = tf.Variable(tf.zeros([10]))
# Construct model
activation = tf.nn.softmax(tf.matmul(x, W) + b) # Softmax
# Minimize error using cross entropy
# Cross entropy
cost = -tf.reduce_sum(y*tf.log(activation))
# Gradient Descent
optimizer = tf.train.GradientDescentOptimizer(learning_rate).minimize(cost)
# Initializing the variables
init = tf.initialize_all_variables()
# Launch the graph
with tf.Session() as sess:
sess.run(init)
# Training cycle
for epoch in range(training_epochs):
avg_cost = 0.
total_batch = int(mnist.train.num_examples/batch_size)
# Loop over all batches
for i in range(total_batch):
batch_xs, batch_ys = mnist.train.next_batch(batch_size)
# Fit training using batch data
sess.run(optimizer, feed_dict={x: batch_xs, y: batch_ys})
# Compute average loss
avg_cost += sess.run(cost, feed_dict={x: batch_xs, y: batch_ys})/total_batch
# Display logs per epoch step
if epoch % display_step == 0:
print "Epoch:", '%04d' % (epoch+1), "cost=", "{:.9f}".format(avg_cost)
print "Optimization Finished!"
# Test model
correct_prediction = tf.equal(tf.argmax(activation, 1), tf.argmax(y, 1))
# Calculate accuracy
accuracy = tf.reduce_mean(tf.cast(correct_prediction, "float"))
print "Accuracy:", accuracy.eval({x: mnist.test.images, y: mnist.test.labels})