q1_softmax.py

import numpy as np
import tensorflow as tf

def softmax(x):
  """
  Compute the softmax function in tensorflow.

  You might find the tensorflow functions tf.exp, tf.reduce_max,
  tf.reduce_sum, tf.expand_dims useful. (Many solutions are possible, so you may
  not need to use all of these functions). Recall also that many common
  tensorflow operations are sugared (e.g. x * y does a tensor multiplication
  if x and y are both tensors). Make sure to implement the numerical stability
  fixes as in the previous homework!

  Args:
    x:   tf.Tensor with shape (n_samples, n_features). Note feature vectors are
         represented by row-vectors. (For simplicity, no need to handle 1-d
         input as in the previous homework)
  Returns:
    out: tf.Tensor with shape (n_sample, n_features). You need to construct this
         tensor in this problem.
  """

  ### YOUR CODE HERE
  maxes = tf.expand_dims(tf.reduce_max(x, reduction_indices=[1]), 1)
  x_red = x - maxes
  x_exp = tf.exp(x_red)
  sums = tf.expand_dims(tf.reduce_sum(x_exp, reduction_indices=[1]), 1)
  out = x_exp / sums 
  ### END YOUR CODE
  
  return out 

def cross_entropy_loss(y, yhat):
  """
  Compute the cross entropy loss in tensorflow.

  y is a one-hot tensor of shape (n_samples, n_classes) and yhat is a tensor
  of shape (n_samples, n_classes). y should be of dtype tf.int32, and yhat should
  be of dtype tf.float32.

  The functions tf.to_float, tf.reduce_sum, and tf.log might prove useful. (Many
  solutions are possible, so you may not need to use all of these functions).

  Note: You are NOT allowed to use the tensorflow built-in cross-entropy
        functions.

  Args:
    y:    tf.Tensor with shape (n_samples, n_classes). One-hot encoded.
    yhat: tf.Tensorwith shape (n_sample, n_classes). Each row encodes a
          probability distribution and should sum to 1.
  Returns:
    out:  tf.Tensor with shape (1,) (Scalar output). You need to construct this
          tensor in the problem.
  """
  ### YOUR CODE HERE
  y = tf.to_float(y)
  out = -tf.reduce_sum(y * tf.log(yhat)) 
  ### END YOUR CODE
  return out


def test_softmax_basic():
  """
  Some simple tests to get you started. 
  Warning: these are not exhaustive.
  """
  print "Running basic tests..."
  test1 = softmax(tf.convert_to_tensor(
      np.array([[1001,1002],[3,4]]), dtype=tf.float32))
  with tf.Session():
      test1 = test1.eval()
  assert np.amax(np.fabs(test1 - np.array(
      [0.26894142,  0.73105858]))) <= 1e-6

  test2 = softmax(tf.convert_to_tensor(
      np.array([[-1001,-1002]]), dtype=tf.float32))
  with tf.Session():
      test2 = test2.eval()
  assert np.amax(np.fabs(test2 - np.array(
      [0.73105858, 0.26894142]))) <= 1e-6

  print "Basic (non-exhaustive) softmax tests pass\n"

def test_cross_entropy_loss_basic():
  """
  Some simple tests to get you started.
  Warning: these are not exhaustive.
  """
  y = np.array([[0, 1], [1, 0], [1, 0]])
  yhat = np.array([[.5, .5], [.5, .5], [.5, .5]])

  test1 = cross_entropy_loss(
      tf.convert_to_tensor(y, dtype=tf.int32),
      tf.convert_to_tensor(yhat, dtype=tf.float32))
  with tf.Session():
    test1 = test1.eval()
  result = -3 * np.log(.5)
  assert np.amax(np.fabs(test1 - result)) <= 1e-6
  print "Basic (non-exhaustive) cross-entropy tests pass\n"

if __name__ == "__main__":
  test_softmax_basic()
  test_cross_entropy_loss_basic()