"""Multi-class Logistic Regression Class

The logistic regression is fully described by a weight matrix :math:`W`

and bias vector :math:`b`. Classification is done by projecting data

points onto a set of hyperplanes, the distance to which is used to

determine a class membership probability.

"""

def __init__(self, input, n_in, n_out, W=None, b=None, temperature=1):

""" Initialize the parameters of the logistic regression

:type input: theano.tensor.TensorType

:param input: symbolic variable that describes the input of the

architecture (one minibatch)

:type n_in: int

:param n_in: number of input units, the dimension of the space in

which the datapoints lie

:type n_out: int

:param n_out: number of output units, the dimension of the space in

which the labels lie

"""

# start-snippet-1

# initialize with 0 the weights W as a matrix of shape (n_in, n_out)

if W is None:

self.W = theano.shared(

value=np.zeros((n_in, n_out), dtype=theano.config.floatX),

name='W',

borrow=True

)

else:

self.W = W

# initialize the baises b as a vector of n_out 0s

if b is None:

self.b = theano.shared(

value=np.zeros((n_out,), dtype=theano.config.floatX),

name='b',

borrow=True

)

else:

self.b = b

# symbolic expression for computing the matrix of class-membership

# probabilities

# Where:

# W is a matrix where column-k represent the separation hyper plain for

# class-k

# x is a matrix where row-j represents input training sample-j

# b is a vector where element-k represent the free parameter of hyper

# plain-k

self.p_y_given_x = T.nnet.softmax(T.dot(input, self.W) + self.b)

self.p_y_given_x_relaxed = T.nnet.softmax(T.dot(input, self.W / temperature) + self.b / temperature)

# symbolic description of how to compute prediction as class whose

# probability is maximal

self.y_pred = T.argmax(self.p_y_given_x, axis=1)

# end-snippet-1

# parameters of the model

self.params = [self.W, self.b]

def negative_log_likelihood(self, y):

"""Return the mean of the negative log-likelihood of the prediction

of this model under a given target distribution.

.. math::

\frac{1}{|\mathcal{D}|} \mathcal{L} (\theta=\{W,b\}, \mathcal{D}) =

\frac{1}{|\mathcal{D}|} \sum_{i=0}^{|\mathcal{D}|}

\log(P(Y=y^{(i)}|x^{(i)}, W,b)) \\

\ell (\theta=\{W,b\}, \mathcal{D})

:type y: theano.tensor.TensorType

:param y: corresponds to a vector that gives for each example the

correct label

Note: we use the mean instead of the sum so that

the learning rate is less dependent on the batch size

"""

# start-snippet-2

# y.shape[0] is (symbolically) the number of rows in y, i.e.,

# number of examples (call it n) in the minibatch

# T.arange(y.shape[0]) is a symbolic vector which will contain

# [0,1,2,... n-1] T.log(self.p_y_given_x) is a matrix of

# Log-Probabilities (call it LP) with one row per example and

# one column per class LP[T.arange(y.shape[0]),y] is a vector

# v containing [LP[0,y[0]], LP[1,y[1]], LP[2,y[2]], ...,

# LP[n-1,y[n-1]]] and T.mean(LP[T.arange(y.shape[0]),y]) is

# the mean (across minibatch examples) of the elements in v,

# i.e., the mean log-likelihood across the minibatch.

return -T.mean(T.log(self.p_y_given_x)[T.arange(y.shape[0]), y])

# end-snippet-2

def errors(self, y):

"""Return a float representing the number of errors in the minibatch

over the total number of examples of the minibatch ; zero one

loss over the size of the minibatch

:type y: theano.tensor.TensorType

:param y: corresponds to a vector that gives for each example the

correct label

"""

# check if y has same dimension of y_pred

if y.ndim != self.y_pred.ndim:

raise TypeError(

'y should have the same shape as self.y_pred',

('y', y.type, 'y_pred', self.y_pred.type)

)

# check if y is of the correct datatype

if y.dtype.startswith('int'):

# the T.neq operator returns a vector of 0s and 1s, where 1

# represents a mistake in prediction

return T.mean(T.neq(self.y_pred, y))

else:

from pylearn2.utils import serial

from pylearn2.datasets.zca_dataset import ZCA_Dataset

# from pylearn2.datasets.cifar10 import CIFAR10

import theano

def rotate_and_convert_grayscale(img):

reshaped = img.reshape(32, 32, 3, order='F')

rotated = np.rot90(reshaped, k=3)

grayscaled = np.dot(rotated[:, :, :3], [0.299, 0.587, 0.144])

return grayscaled

def transform(img_set):

result = []

# Convert all images to grayscale and flatten the shape

for img in img_set:

# result.append(rotate_and_convert_grayscale(img).ravel())

result.append(img.ravel())

return np.array(result)

# train_set = CIFAR10(which_set='train', start=0, stop=45000)

# valid_set = CIFAR10(which_set='train', start=45000, stop=50000)

# test_set = CIFAR10(which_set='test')

data_path = os.getenv('PYLEARN2_DATA_PATH')

whitened_path = os.path.join(data_path, 'cifar10_cpu', 'pylearn2_gcn_whitened')

preprocessed_train_dataset = serial.load(os.path.join(whitened_path, 'train.pkl'))

preprocessed_test_dataset = serial.load(os.path.join(whitened_path, 'test.pkl'))

preprocesssor = serial.load(os.path.join(whitened_path, 'preprocessor.pkl'))

train_set = ZCA_Dataset(preprocessed_train_dataset, preprocesssor, start=0, stop=45000)

valid_set = ZCA_Dataset(preprocessed_train_dataset, preprocesssor, start=45000, stop=50000)

test_set = ZCA_Dataset(preprocessed_test_dataset, preprocesssor)

# Convert the images to grayscale and flatten them

train_set.X = transform(train_set.X)

valid_set.X = transform(valid_set.X)

test_set.X = transform(test_set.X)

def shared_y_cast(y):

shared_y = theano.shared(np.asarray(y, dtype=theano.config.floatX), borrow=True)

return T.cast(shared_y, 'int32')

train_set_tuple = (theano.shared(np.array(train_set.X, dtype=theano.config.floatX), borrow=True),

shared_y_cast(train_set.y.ravel()))

valid_set_tuple = (theano.shared(np.array(valid_set.X, dtype=theano.config.floatX), borrow=True),

shared_y_cast(valid_set.y.ravel()))

test_set_tuple = (theano.shared(np.array(test_set.X, dtype=theano.config.floatX), borrow=True),

shared_y_cast(test_set.y.ravel()))

from pylearn2.datasets.zca_dataset import ZCA_Dataset

from pylearn2.utils import serial

import theano

import theano.tensor as T

def flatten(img_set):

result = []

for img in img_set:

result.append(img.ravel())

return np.array(result)

def shared_y_cast(y):

shared_y = theano.shared(np.asarray(y, dtype=theano.config.floatX), borrow=True)

return T.cast(shared_y, 'int32')

whitened_path = os.path.join(cifar_path, 'pylearn2_gcn_whitened')

preprocessed_train_dataset = serial.load(os.path.join(whitened_path, 'train.pkl'))

preprocessed_test_dataset = serial.load(os.path.join(whitened_path, 'test.pkl'))

preprocesssor = serial.load(os.path.join(whitened_path, 'preprocessor.pkl'))

train_set = ZCA_Dataset(preprocessed_train_dataset, preprocesssor, start=0, stop=45000)

valid_set = ZCA_Dataset(preprocessed_train_dataset, preprocesssor, start=45000, stop=50000)

test_set = ZCA_Dataset(preprocessed_test_dataset, preprocesssor)

if confidence_ascending is not None:

X_new = np.empty_like(train_set.X)

y_new = np.empty_like(train_set.y)

for i in range(len(X_new)):

label = int(train_set.y[i])

index_new = confidence_ascending[label].pop(0)

X_new[i] = train_set.X[index_new]

y_new[i] = train_set.y[index_new]

train_set.X = X_new

train_set.y = y_new

train_set.X = flatten(train_set.X)

valid_set.X = flatten(valid_set.X)

test_set.X = flatten(test_set.X)

train_set_tuple = \

theano.shared(np.array(train_set.X, dtype=theano.config.floatX), borrow=True), \

shared_y_cast(train_set.y.ravel())

valid_set_tuple = \

theano.shared(np.array(valid_set.X, dtype=theano.config.floatX), borrow=True), \

shared_y_cast(valid_set.y.ravel())

test_set_tuple = \

theano.shared(np.array(test_set.X, dtype=theano.config.floatX), borrow=True), \

shared_y_cast(test_set.y.ravel())

""" Loads the dataset

:type dataset: string

:param dataset: the path to the dataset (here MNIST)

"""

#############

# LOAD DATA #

#############

# Download the MNIST dataset if it is not present

data_dir, data_file = os.path.split(dataset)

if data_dir == "" and not os.path.isfile(dataset):

# Check if dataset is in the data directory.

new_path = os.path.join(

os.path.split(__file__)[0],

"..",

"data",

dataset

)

if os.path.isfile(new_path) or data_file == 'mnist.pkl.gz':

dataset = new_path

if (not os.path.isfile(dataset)) and data_file == 'mnist.pkl.gz':

import urllib

origin = (

'http://www.iro.umontreal.ca/~lisa/deep/data/mnist/mnist.pkl.gz'

)

print 'Downloading data from %s' % origin

urllib.urlretrieve(origin, dataset)

print '... loading data'

# Load the dataset

f = gzip.open(dataset, 'rb')

train_set, valid_set, test_set = cPickle.load(f)

f.close()

# train_set, valid_set, test_set format: tuple(input, target)

# input is an numpy.ndarray of 2 dimensions (a matrix)

# witch row's correspond to an example. target is a

# numpy.ndarray of 1 dimensions (vector)) that have the same length as

# the number of rows in the input. It should give the target

# target to the example with the same index in the input.

if confidence_ascending is not None:

X_new = np.empty_like(train_set[0])

y_new = np.empty_like(train_set[1])

for i in range(len(X_new)):

label = train_set[1][i]

index_new = confidence_ascending[label].pop(0)

X_new[i] = train_set[0][index_new]

y_new[i] = train_set[1][index_new]

train_set = (X_new, y_new)

def shared_dataset(data_xy, borrow=True):

""" Function that loads the dataset into shared variables

The reason we store our dataset in shared variables is to allow

Theano to copy it into the GPU memory (when code is run on GPU).

Since copying data into the GPU is slow, copying a minibatch everytime

is needed (the default behaviour if the data is not in a shared

variable) would lead to a large decrease in performance.

"""

data_x, data_y = data_xy

shared_x = theano.shared(np.asarray(data_x,

dtype=theano.config.floatX),

borrow=borrow)

shared_y = theano.shared(np.asarray(data_y,

dtype=theano.config.floatX),

borrow=borrow)

# When storing data on the GPU it has to be stored as floats

# therefore we will store the labels as ``floatX`` as well

# (``shared_y`` does exactly that). But during our computations

# we need them as ints (we use labels as index, and if they are

# floats it doesn't make sense) therefore instead of returning

# ``shared_y`` we will have to cast it to int. This little hack

# lets ous get around this issue

return shared_x, T.cast(shared_y, 'int32')

test_set_x, test_set_y = shared_dataset(test_set)

valid_set_x, valid_set_y = shared_dataset(valid_set)

train_set_x, train_set_y = shared_dataset(train_set)

rval = [(train_set_x, train_set_y), (valid_set_x, valid_set_y),

(test_set_x, test_set_y)]

dataset='mnist.pkl.gz',

batch_size=600):

"""

Demonstrate stochastic gradient descent optimization of a log-linear

model

This is demonstrated on MNIST.

:type learning_rate: float

:param learning_rate: learning rate used (factor for the stochastic

gradient)

:type n_epochs: int

:param n_epochs: maximal number of epochs to run the optimizer

:type dataset: string

:param dataset: the path of the MNIST dataset file from

http://www.iro.umontreal.ca/~lisa/deep/data/mnist/mnist.pkl.gz

"""

datasets = load_data(dataset)

train_set_x, train_set_y = datasets[0]

valid_set_x, valid_set_y = datasets[1]

test_set_x, test_set_y = datasets[2]

# compute number of minibatches for training, validation and testing

n_train_batches = train_set_x.get_value(borrow=True).shape[0] / batch_size

n_valid_batches = valid_set_x.get_value(borrow=True).shape[0] / batch_size

n_test_batches = test_set_x.get_value(borrow=True).shape[0] / batch_size

######################

# BUILD ACTUAL MODEL #

######################

print '... building the model'

# allocate symbolic variables for the data

index = T.lscalar() # index to a [mini]batch

# generate symbolic variables for input (x and y represent a

# minibatch)

x = T.matrix('x') # data, presented as rasterized images

y = T.ivector('y') # labels, presented as 1D vector of [int] labels

# construct the logistic regression class

# Each MNIST image has size 28*28

classifier = LogisticRegression(input=x, n_in=28 * 28, n_out=10)

# the cost we minimize during training is the negative log likelihood of

# the model in symbolic format

cost = classifier.negative_log_likelihood(y)

# compiling a Theano function that computes the mistakes that are made by

# the model on a minibatch

test_model = theano.function(

inputs=[index],

outputs=classifier.errors(y),

givens={

x: test_set_x[index * batch_size: (index + 1) * batch_size],

y: test_set_y[index * batch_size: (index + 1) * batch_size]

}

)

validate_model = theano.function(

inputs=[index],

outputs=classifier.errors(y),

givens={

x: valid_set_x[index * batch_size: (index + 1) * batch_size],

y: valid_set_y[index * batch_size: (index + 1) * batch_size]

}

)

# compute the gradient of cost with respect to theta = (W,b)

g_W = T.grad(cost=cost, wrt=classifier.W)

g_b = T.grad(cost=cost, wrt=classifier.b)

# start-snippet-3

# specify how to update the parameters of the model as a list of

# (variable, update expression) pairs.

updates = [(classifier.W, classifier.W - learning_rate * g_W),

(classifier.b, classifier.b - learning_rate * g_b)]

# compiling a Theano function `train_model` that returns the cost, but in

# the same time updates the parameter of the model based on the rules

# defined in `updates`

train_model = theano.function(

inputs=[index],

outputs=cost,

updates=updates,

givens={

x: train_set_x[index * batch_size: (index + 1) * batch_size],

y: train_set_y[index * batch_size: (index + 1) * batch_size]

}

)

# end-snippet-3

###############

# TRAIN MODEL #

###############

print '... training the model'

# early-stopping parameters

patience = 5000 # look as this many examples regardless

patience_increase = 2 # wait this much longer when a new best is

# found

improvement_threshold = 0.995 # a relative improvement of this much is

# considered significant

validation_frequency = min(n_train_batches, patience / 2)

# go through this many

# minibatche before checking the network

# on the validation set; in this case we

# check every epoch

best_validation_loss = np.inf

test_score = 0.

start_time = time.clock()

done_looping = False

epoch = 0

while (epoch < n_epochs) and (not done_looping):

epoch = epoch + 1

for minibatch_index in xrange(n_train_batches):

minibatch_avg_cost = train_model(minibatch_index)

# iteration number

iter = (epoch - 1) * n_train_batches + minibatch_index

if (iter + 1) % validation_frequency == 0:

# compute zero-one loss on validation set

validation_losses = [validate_model(i)

for i in xrange(n_valid_batches)]

this_validation_loss = np.mean(validation_losses)

print(

'epoch %i, minibatch %i/%i, validation error %f %%' %

(

epoch,

minibatch_index + 1,

n_train_batches,

this_validation_loss * 100.

)

)

# if we got the best validation score until now

if this_validation_loss < best_validation_loss:

# improve patience if loss improvement is good enough

if this_validation_loss < best_validation_loss * \

improvement_threshold:

patience = max(patience, iter * patience_increase)

best_validation_loss = this_validation_loss

# test it on the test set

test_losses = [test_model(i)

for i in xrange(n_test_batches)]

test_score = np.mean(test_losses)

print(

(

' epoch %i, minibatch %i/%i, test error of'

' best model %f %%'

) %

(

epoch,

minibatch_index + 1,

n_train_batches,

test_score * 100.

)

)

if patience <= iter:

done_looping = True

break

end_time = time.clock()

print(

(

'Optimization complete with best validation score of %f %%,'

'with test performance %f %%'

)

% (best_validation_loss * 100., test_score * 100.)

)

print 'The code run for %d epochs, with %f epochs/sec' % (

epoch, 1. * epoch / (end_time - start_time))

print >> sys.stderr, ('The code for file ' +

os.path.split(__file__)[1] +