Basic Linear Regression with Theano

linreg.py

# (CC-NC-SA) Nasim Rahaman 

import theano as th
import theano.tensor as T
import numpy as np
import time

# Weights
W = th.shared(value=np.random.uniform(size=(3, 3)))
# Input
x = T.matrix()
# Output
y = T.dot(x, W)
# Target
yt = T.matrix()
# MSE Loss
L = T.mean(T.sum((y - yt) ** 2, axis=1))
# Compute Symbolic Gradient
dLdW = T.grad(cost=L, wrt=W)
# Gradient Descent Updates (Learning Rate = 1 works fine)
upd = [(W, W - dLdW)]

# Compile Training Function
train = th.function(inputs=[x, yt], outputs=L, updates=upd, allow_input_downcast=True)

# Generate Synthetic Data (numerical)
numW = np.random.uniform(size=(3, 3))
numx = np.random.uniform(size=(100, 3))
numyt = np.dot(numx, numW)

print("Initial W: \n {}".format(W.get_value()))
print("Target W: \n {}".format(numW))

programstart = time.time()

# Batch gradient descent for 500 epochs
for _ in xrange(500):
    train(numx, numyt)

programstop = time.time()

print("Fitted W: \n {}".format(W.get_value()))


print("Elapsed Time: {} seconds on a GPU (GT 750M)".format(programstop - programstart))

# Using gpu device 0: GeForce GT 750M
# Initial W:
#  [[ 0.36780546  0.70396992  0.36098496]
#  [ 0.04568252  0.60477838  0.47389695]
#  [ 0.69876337  0.92058904  0.57620348]]
# Target W:
#  [[ 0.28928668  0.67040456  0.20592429]
#  [ 0.98262113  0.37950274  0.50209176]
#  [ 0.27904913  0.88948569  0.38525592]]
# Fitted W:
#  [[ 0.28928668  0.67040456  0.20592429]
#  [ 0.98262113  0.37950274  0.50209176]
#  [ 0.27904913  0.88948569  0.38525592]]
# Elapsed Time: 0.154557228088 seconds on a GPU (GT 750M)