Notes for machine learning

theano.py

#!/bin/env python

# Just playing with theano. This doesn't do anything particularly useful
# other than showing how things work

import numpy
import theano
import theano.tensor as T
from theano import function

# Creates variables and the operations
x = T.dscalar()
y = T.dmatrix('y')
z = x + y

# List of parameters followed by the gra
f = function([x, y], z)  # Compiles an executable function

print(f(2, [[1, 2], [3,4]]))

# Logistic equation
x = T.dmatrix('x')
s = 1 / (1 + T.exp(-x))  # 1 / (1 + e^-x)
logistic = function([x], s)

m_1 = [[1, 1], [2, 2]]
m_2 = [[1, 1], [2, 3]]

print(logistic(m_1))
print(logistic(m_2))

# Create multiple matrices simultaneously
a, b = T.dmatrices('a', 'b')

# bunch of functions
diff = a - b
abs_diff = abs(diff)
diff_sqr = diff * diff

f = function([a, b], [diff, abs_diff, diff_sqr])  # Will execute all three in one shot

# Shared variables
# ------------------------
from theano import shared

state = shared(0)  # shared variable
inc = T.iscalar('inc')  # Incrementer variable

# one tuple in updates for every shared variable
f = function([inc], state, updates=[(state, state+inc)])

# Full Logistic regression
# ---------------------------

rng = numpy.random
N = 400  # Number of rows
features = 700  # Features

# The dataset
D = (rng.randn(N, features), rng.randint(size=N, low=0, high=2))

training_steps = 10000

x = T.dmatrix('x')
y = T.dvector('y')

w = shared(rng.randn(features), name='weights')
# Don't forget the decimal, it will be an integer otherwise and mess everything up
b = shared(0., name='b')

# Predictions
p_1 = 1 / (1 + T.exp(-T.dot(x, w) - b))
prediction = p_1 > 0.5

# cross entropy
xent = -y * T.log(p_1) - (1 - y) * T.log(1 - p_1)

# cost function to effect the gradients -- minimize cost
cost = xent.mean() + 0.01 * (w ** 2).sum()

# Gradients for weights and bias
gw, gb = T.grad(cost, [w, b])

# Put it all together
train = function(inputs=[x, y], outputs=[prediction, xent], updates=[(w, w - 0.1 * gw), (b, b - 0.1  * gb)])
predict = function(inputs=[x], outputs=[prediction])

# Now we need to run it -- train!
# We'll ignore the prediction and error outputs for now
for i in range(training_steps):
    pred, err = train()

# Now predict -- run it in a useful way
prediction(D[0])