--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/code_tutoriel/logistic_cg.py	Fri Feb 26 13:55:27 2010 -0500
@@ -0,0 +1,310 @@
+"""
+This tutorial introduces logistic regression using Theano and conjugate 
+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, and a conjugate gradient optimization method 
+that is suitable for smaller datasets.
+
+
+References:
+
+   - textbooks: "Pattern Recognition and Machine Learning" - 
+                 Christopher M. Bishop, section 4.3.2
+
+
+"""
+__docformat__ = 'restructedtext en'
+
+
+import numpy, time, cPickle, gzip
+
+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 datapoint lies
+
+        :type n_out: int
+        :param n_out: number of output units, the dimension of the space in 
+                      which the target lies
+
+        """ 
+
+        # initialize theta = (W,b) with 0s; W gets the shape (n_in, n_out), 
+        # while b is a vector of n_out elements, making theta a vector of
+        # n_in*n_out + n_out elements
+        self.theta = theano.shared( value = numpy.zeros(n_in*n_out+n_out, dtype = theano.config.floatX) )
+        # W is represented by the fisr n_in*n_out elements of theta
+        self.W     = self.theta[0:n_in*n_out].reshape((n_in,n_out))
+        # b is the rest (last n_out elements)
+        self.b     = self.theta[n_in*n_out:n_in*n_out+n_out]
+
+
+        # compute vector of class-membership probabilities in symbolic form
+        self.p_y_given_x = T.nnet.softmax(T.dot(input, self.W)+self.b)
+
+        # compute prediction as class whose probability is maximal in 
+        # symbolic form
+        self.y_pred=T.argmax(self.p_y_given_x, axis=1)
+
+
+
+
+
+    def negative_log_likelihood(self, y):
+        """Return 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
+        """
+        return -T.mean(T.log(self.p_y_given_x)[T.arange(y.shape[0]),y])
+
+
+
+
+
+    def errors(self, y):
+        """Return a float representing the number of errors in the minibatch 
+        over the total number of examples 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', target.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:
+            raise NotImplementedError()
+
+
+
+
+
+
+
+def cg_optimization_mnist( n_epochs=50, mnist_pkl_gz='mnist.pkl.gz' ):
+    """Demonstrate conjugate gradient optimization of a log-linear model 
+
+    This is demonstrated on MNIST.
+    
+    :type n_epochs: int
+    :param n_epochs: number of epochs to run the optimizer 
+
+    :type mnist_pkl_gz: string
+    :param mnist_pkl_gz: the path of the mnist training file from 
+                         http://www.iro.umontreal.ca/~lisa/deep/data/mnist/mnist.pkl.gz
+
+    """
+    #############
+    # LOAD DATA #
+    #############
+    print '... loading data'
+
+    # Load the dataset 
+    f = gzip.open(mnist_pkl_gz,'rb')
+    train_set, valid_set, test_set = cPickle.load(f)
+    f.close()
+
+    def shared_dataset(data_xy):
+        """ 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(numpy.asarray(data_x, dtype=theano.config.floatX))
+        shared_y = theano.shared(numpy.asarray(data_y, dtype=theano.config.floatX))
+        # 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)
+
+    batch_size = 600    # size of the minibatch
+
+    n_train_batches = train_set_x.value.shape[0] / batch_size
+    n_valid_batches = valid_set_x.value.shape[0] / batch_size
+    n_test_batches  = test_set_x.value.shape[0]  / batch_size
+
+
+    ishape     = (28,28) # this is the size of MNIST images
+    n_in       = 28*28   # number of input units
+    n_out      = 10      # number of output units
+
+
+    ######################
+    # BUILD ACTUAL MODEL #
+    ###################### 
+    print '... building the model'
+
+    # allocate symbolic variables for the data
+    minibatch_offset = T.lscalar() # offset to the start of a [mini]batch 
+    x = T.matrix()   # the data is presented as rasterized images
+    y = T.ivector()  # the labels are presented as 1D vector of 
+                     # [int] labels
+
+ 
+    # construct the logistic regression class
+    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).mean() 
+
+    # compile a theano function that computes the mistakes that are made by 
+    # the model on a minibatch
+    test_model = theano.function([minibatch_offset], classifier.errors(y),
+            givens={
+                x:test_set_x[minibatch_offset:minibatch_offset+batch_size],
+                y:test_set_y[minibatch_offset:minibatch_offset+batch_size]})
+
+    validate_model = theano.function([minibatch_offset],classifier.errors(y),
+            givens={
+                x:valid_set_x[minibatch_offset:minibatch_offset+batch_size],
+                y:valid_set_y[minibatch_offset:minibatch_offset+batch_size]})
+
+    #  compile a thenao function that returns the cost of a minibatch 
+    batch_cost = theano.function([minibatch_offset], cost, 
+            givens= {
+                x : train_set_x[minibatch_offset:minibatch_offset+batch_size],
+                y : train_set_y[minibatch_offset:minibatch_offset+batch_size]})
+
+
+    
+    # compile a theano function that returns the gradient of the minibatch 
+    # with respect to theta
+    batch_grad = theano.function([minibatch_offset], T.grad(cost,classifier.theta), 
+            givens= {
+                x : train_set_x[minibatch_offset:minibatch_offset+batch_size],
+                y : train_set_y[minibatch_offset:minibatch_offset+batch_size]})
+
+
+    # creates a function that computes the average cost on the training set
+    def train_fn(theta_value):
+        classifier.theta.value = theta_value
+        train_losses = [batch_cost(i*batch_size) for i in xrange(n_train_batches)]
+        return numpy.mean(train_losses)
+
+    # creates a function that computes the average gradient of cost with 
+    # respect to theta
+    def train_fn_grad(theta_value):
+        classifier.theta.value = theta_value
+        grad = batch_grad(0)
+        for i in xrange(1,n_train_batches):
+            grad += batch_grad(i*batch_size)
+        return grad/n_train_batches
+
+
+    validation_scores = [float('inf'), 0]
+ 
+    # creates the validation function
+    def callback(theta_value):
+        classifier.theta.value = theta_value
+        #compute the validation loss
+        validation_losses = [validate_model(i*batch_size) for i in xrange(n_valid_batches)]
+        this_validation_loss = numpy.mean(validation_losses)
+        print('validation error %f %%' % (this_validation_loss*100.,))
+        
+        # check if it is better then best validation score got until now
+        if this_validation_loss < validation_scores[0]:
+            # if so, replace the old one, and compute the score on the 
+            # testing dataset
+            validation_scores[0] = this_validation_loss
+            test_loses = [test_model(i*batch_size) for i in xrange(n_test_batches)]
+            validation_scores[1] = numpy.mean(test_loses)
+
+    ###############
+    # TRAIN MODEL #
+    ###############
+ 
+    # using scipy conjugate gradient optimizer 
+    import scipy.optimize
+    print ("Optimizing using scipy.optimize.fmin_cg...")
+    start_time = time.clock()
+    best_w_b = scipy.optimize.fmin_cg(
+               f        = train_fn, 
+               x0       = numpy.zeros((n_in+1)*n_out, dtype=x.dtype),
+               fprime   = train_fn_grad,
+               callback = callback,
+               disp     = 0,
+               maxiter  = n_epochs)
+    end_time = time.clock()
+    print(('Optimization complete with best validation score of %f %%, with '
+          'test performance %f %%') % 
+               (validation_scores[0]*100., validation_scores[1]*100.))
+
+    print ('The code ran for %f minutes' % ((end_time-start_time)/60.))
+
+
+if __name__ == '__main__':
+    cg_optimization_mnist()
+