--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/code_tutoriel/logistic_cg.py	Thu Jan 21 11:26:43 2010 -0500
@@ -0,0 +1,282 @@
+"""
+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, cPickle, gzip
+
+import time
+
+import theano
+import theano.tensor as T
+import theano.tensor.nnet
+
+
+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
+
+        :param input: symbolic variable that describes the input of the 
+        architecture ( one minibatch)
+
+        :param n_in: number of input units, the dimension of the space in 
+        which the datapoint lies
+
+        :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) )
+        # 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}) 
+
+
+        :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 
+        """
+
+        # 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_iter=50 ):
+    """Demonstrate conjugate gradient optimization of a log-linear model 
+
+    This is demonstrated on MNIST.
+    
+    :param n_iter: number of iterations ot run the optimizer 
+
+    """
+
+    # Load the dataset 
+    f = gzip.open('mnist.pkl.gz','rb')
+    train_set, valid_set, test_set = cPickle.load(f)
+    f.close()
+
+    # make minibatches of size 20 
+    batch_size = 20    # sized of the minibatch
+
+    # Dealing with the training set
+    # get the list of training images (x) and their labels (y)
+    (train_set_x, train_set_y) = train_set
+    # initialize the list of training minibatches with empty list
+    train_batches = []
+    for i in xrange(0, len(train_set_x), batch_size):
+        # add to the list of minibatches the minibatch starting at 
+        # position i, ending at position i+batch_size
+        # a minibatch is a pair ; the first element of the pair is a list 
+        # of datapoints, the second element is the list of corresponding 
+        # labels
+        train_batches = train_batches + \
+               [(train_set_x[i:i+batch_size], train_set_y[i:i+batch_size])]
+
+    # Dealing with the validation set
+    (valid_set_x, valid_set_y) = valid_set
+    # initialize the list of validation minibatches 
+    valid_batches = []
+    for i in xrange(0, len(valid_set_x), batch_size):
+        valid_batches = valid_batches + \
+               [(valid_set_x[i:i+batch_size], valid_set_y[i:i+batch_size])]
+
+    # Dealing with the testing set
+    (test_set_x, test_set_y) = test_set
+    # initialize the list of testing minibatches 
+    test_batches = []
+    for i in xrange(0, len(test_set_x), batch_size):
+        test_batches = test_batches + \
+              [(test_set_x[i:i+batch_size], test_set_y[i:i+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
+    # allocate symbolic variables for the data
+    x = T.fmatrix()  # the data is presented as rasterized images
+    y = T.lvector()  # the labels are presented as 1D vector of 
+                          # [long int] labels
+
+ 
+    # construct the logistic regression class
+    classifier = LogisticRegression( \
+                   input=x.reshape((batch_size,28*28)), 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([x,y], classifier.errors(y))
+    # compile a theano function that returns the gradient of the minibatch 
+    # with respect to theta
+    batch_grad = theano.function([x, y], T.grad(cost, classifier.theta))
+    #  compile a thenao function that returns the cost of a minibatch
+    batch_cost = theano.function([x, y], cost)
+
+    # creates a function that computes the average cost on the training set
+    def train_fn(theta_value):
+        classifier.theta.value = theta_value
+        cost = 0.
+        for x,y in train_batches :
+            cost += batch_cost(x,y)
+        return cost / len(train_batches)
+
+    # 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 = numpy.zeros(n_in * n_out + n_out)
+        for x,y in train_batches:
+            grad += batch_grad(x,y)
+        return grad/ len(train_batches)
+
+
+
+    validation_scores = [float('inf'), 0]
+ 
+    # creates the validation function
+    def callback(theta_value):
+        classifier.theta.value = theta_value
+        #compute the validation loss
+        this_validation_loss = 0.
+        for x,y in valid_batches:
+            this_validation_loss += test_model(x,y)
+
+        this_validation_loss /= len(valid_batches)
+
+        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_score = 0.
+            for x,y in test_batches:
+                test_score += test_model(x,y)
+            validation_scores[1] = test_score / len(test_batches)
+
+    # 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_iter)
+    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()
+