# coding=utf-8#
"""
This tutorial introduces logistic regression using Theano and stochastic
gradient descent.
Logistic regression is a probabilistic, linear classifier. It is parametrized
by a weight matrix :math:`W` and a 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.
Mathematically, this can be written as:
.. math::
P(Y=i|x, W,b) &= softmax_i(W x + b) \\
&= \frac {e^{W_i x + b_i}} {\sum_j e^{W_j x + b_j}}
The output of the model or prediction is then done by taking the argmax of
the vector whose i'th element is P(Y=i|x).
.. math::
y_{pred} = argmax_i P(Y=i|x,W,b)
This tutorial presents a stochastic gradient descent optimization method
suitable for large datasets.
References:
- textbooks: "Pattern Recognition and Machine Learning" -
Christopher M. Bishop, section 4.3.2
"""
from __future__ import print_function #可以通过 import __future__ 来将2.7版本的print语句移除,让你可以Python3.x的print()功能函数的形式。例如:
__docformat__ = 'restructedtext en'
import six.moves.cPickle as pickle
import gzip
import os
import sys
import timeit
import numpy
import theano
import theano.tensor as T
class LogisticRegression(object):
"""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):
""" 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)
self.W = theano.shared(
value=numpy.zeros(
(n_in, n_out),
dtype=theano.config.floatX # for GPU
),
name='W',
borrow=True # dont copy the large dataset in the memory
)
# initialize the biases b as a vector of n_out 0s
self.b = theano.shared(
value=numpy.zeros(
(n_out,),
dtype=theano.config.floatX
),
name='b',
borrow=True
)
# symbolic expression for computing the matrix of class-membership
# probabilities
# Where:
# W is a matrix where column-k represent the separation hyperplane 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
# hyperplane-k
self.p_y_given_x = T.nnet.softmax(T.dot(input, self.W) + self.b)
# 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]
# keep track of model input
self.input = input
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.
# T.arange(y.shape[0])返回的是一个向量[0,1,...,len(y)],y也是一个向量,如[3,5,6...,9],代表的是所属的类别
return -T.mean(T.log(self.p_y_given_x)[T.arange(y.shape[0]), y])# T.log(self.p_y_given_x)[T.arange(y.shape[0]), y]表示的是T.log(self.p_y_given_x)[0,3],mean函数内部是一个向量
# 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)) # a neq ual (a!=b)
else:
raise NotImplementedError()
def load_data(dataset):
''' 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':
from six.moves import urllib
origin = (
'http://www.iro.umontreal.ca/~lisa/deep/data/mnist/mnist.pkl.gz'
)
print('Downloading data from %s' % origin)
urllib.request.urlretrieve(origin, dataset)
print('... loading data')
# Load the dataset
with gzip.open(dataset, 'rb') as f:
try:
train_set, valid_set, test_set = pickle.load(f, encoding='latin1')
except:
train_set, valid_set, test_set = pickle.load(f)
# train_set, valid_set, test_set format: tuple(input, target)
# input is a numpy.ndarray of 2 dimensions (a matrix)
# where each row c