Justonepixel.com - Linear regression in a >1D vector space

Linear regression in a >1D vector space posted on 03 July 2017

This is a simple example of running a linear regression on a vector space with more than one dimension.

The main take away on my end is that the * operator is overwritten with the product between tensors, not matrices - if you think about how training is done with batches, it totally make sense though.. Hopefully if you did study a lot of linear algebra but not so much tensors, you won’t have to waste time trying to figure out why your regression converge to such weird values.

import tensorflow as tf
import random

def generate_test_case(sess, input_size, output_size):
  new_input = []
  for j in range(input_size):
    new_input.append(random.randrange(-50, 50))

  # Define the model we are interested to discover.
  # This assums input_size=2 and output_size=3
  W = tf.constant([1, 2, 3, 4, 5, 6], shape=[2, 3])
  b = tf.constant([10, 13, 22], shape=[1, 3])

  x = tf.constant(new_input, shape=[1, 2])
  test = tf.matmul(x, W) + b
  new_output = sess.run(test)[0]

  return new_input, new_output

def main(input_size, output_size):
  # Generate the linear model we want to build.
  x = tf.placeholder(tf.float32, [None, input_size], name='x')
  W = tf.Variable(tf.zeros([input_size, output_size]))
  b = tf.Variable(tf.zeros([output_size]))
  model = tf.matmul(x, W) + b

  # Build the loss function.
  sess = tf.Session()
  y = tf.placeholder(tf.float32, [None, output_size], name='y')
  squared_deltas = tf.square(model - y)
  loss = tf.reduce_mean(squared_deltas)

  # Define how we'll optimize W.
  init = tf.global_variables_initializer()
  optimizer = tf.train.GradientDescentOptimizer(0.001)
  train = optimizer.minimize(loss)
  sess.run(init)

  num_training_cases = 100 # Number of training cases
  train_input = []
  train_output = []
  for i in range(num_training_cases):
    new_input, new_output = generate_test_case(sess, input_size, output_size)
    train_input.append(new_input)
    train_output.append(new_output)

  print('Initial loss %d' % sess.run(loss, feed_dict={x:train_input, y:train_output}))
  print()

  for i in range(10000):
    sess.run(train, {x:train_input, y:train_output})

  print('---------------------')
  print('W\n %s' % sess.run(W))
  print('b\n %s'% sess.run(b))
  print('Loss %d' % sess.run(loss, feed_dict={x:train_input, y:train_output}))
  print()

  print('---------------------')
  print('Evaluating with a single case')
  eval_input, eval_output = generate_test_case(sess, input_size, output_size)
  print(eval_input)
  print(eval_output)
  print(sess.run(model, {x:[eval_input]}))
  print('Loss %d' % sess.run(loss, feed_dict={x:[eval_input], y:[eval_output]}))

if __name__ == "__main__":
  main(2, 3)

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