--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/code_tutoriel/mlp.py	Thu Jan 21 11:26:43 2010 -0500
@@ -0,0 +1,331 @@
+"""
+This tutorial introduces the multilayer perceptron using Theano.  
+
+ A multilayer perceptron is a logistic regressor where
+instead of feeding the input to the logistic regression you insert a
+intermidiate layer, called the hidden layer, that has a nonlinear 
+activation function (usually tanh or sigmoid) . One can use many such 
+hidden layers making the architecture deep. The tutorial will also tackle 
+the problem of MNIST digit classification.
+
+.. math::
+
+    f(x) = G( b^{(2)} + W^{(2)}( s( b^{(1)} + W^{(1)} x))),
+
+References:
+
+    - textbooks: "Pattern Recognition and Machine Learning" - 
+                 Christopher M. Bishop, section 5
+
+TODO: recommended preprocessing, lr ranges, regularization ranges (explain 
+      to do lr first, then add regularization)
+
+"""
+__docformat__ = 'restructedtext en'
+
+
+import numpy, cPickle, gzip
+
+
+import theano
+import theano.tensor as T
+
+import time 
+
+import theano.tensor.nnet
+
+class MLP(object):
+    """Multi-Layer Perceptron Class
+
+    A multilayer perceptron is a feedforward artificial neural network model 
+    that has one layer or more of hidden units and nonlinear activations. 
+    Intermidiate layers usually have as activation function thanh or the 
+    sigmoid function  while the top layer is a softamx layer. 
+    """
+
+
+
+    def __init__(self, input, n_in, n_hidden, n_out):
+        """Initialize the parameters for the multilayer perceptron
+
+        :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 datapoints lie
+
+        :param n_hidden: number of hidden units 
+
+        :param n_out: number of output units, the dimension of the space in 
+        which the labels lie
+
+        """
+
+        # initialize the parameters theta = (W1,b1,W2,b2) ; note that this 
+        # example contains only one hidden layer, but one can have as many 
+        # layers as he/she wishes, making the network deeper. The only 
+        # problem making the network deep this way is during learning, 
+        # backpropagation being unable to move the network from the starting
+        # point towards; this is where pre-training helps, giving a good 
+        # starting point for backpropagation, but more about this in the 
+        # other tutorials
+        
+        # `W1` is initialized with `W1_values` which is uniformely sampled
+        # from -1/sqrt(n_in) and 1/sqrt(n_in)
+        # the output of uniform if converted using asarray to dtype 
+        # theano.config.floatX so that the code is runable on GPU
+        W1_values = numpy.asarray( numpy.random.uniform( \
+              low = -numpy.sqrt(6./(n_in+n_hidden)), high = numpy.sqrt(6./(n_in+n_hidden)), \
+              size = (n_in, n_hidden)), dtype = theano.config.floatX)
+        # `W2` is initialized with `W2_values` which is uniformely sampled 
+        # from -1/sqrt(n_hidden) and 1/sqrt(n_hidden)
+        # the output of uniform if converted using asarray to dtype 
+        # theano.config.floatX so that the code is runable on GPU
+        W2_values = numpy.asarray( numpy.random.uniform( 
+              low = numpy.sqrt(6./(n_hidden+n_out)), high= numpy.sqrt(6./(n_hidden+n_out)),\
+              size= (n_hidden, n_out)), dtype = theano.config.floatX)
+
+        self.W1 = theano.shared( value = W1_values )
+        self.b1 = theano.shared( value = numpy.zeros((n_hidden,), 
+                                                dtype= theano.config.floatX))
+        self.W2 = theano.shared( value = W2_values )
+        self.b2 = theano.shared( value = numpy.zeros((n_out,), 
+                                                dtype= theano.config.floatX))
+
+        # symbolic expression computing the values of the hidden layer
+        self.hidden = T.tanh(T.dot(input, self.W1)+ self.b1)
+
+        # symbolic expression computing the values of the top layer 
+        self.p_y_given_x= T.nnet.softmax(T.dot(self.hidden, self.W2)+self.b2)
+
+        # compute prediction as class whose probability is maximal in 
+        # symbolic form
+        self.y_pred = T.argmax( self.p_y_given_x, axis =1)
+        
+        # L1 norm ; one regularization option is to enforce L1 norm to 
+        # be small 
+        self.L1     = abs(self.W1).sum() + abs(self.W2).sum()
+
+        # square of L2 norm ; one regularization option is to enforce 
+        # square of L2 norm to be small
+        self.L2_sqr = (self.W1**2).sum() + (self.W2**2).sum()
+
+
+
+    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}) 
+
+
+        :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 sgd_optimization_mnist( learning_rate=0.01, L1_reg = 0.00, \
+                            L2_reg = 0.0001, n_iter=100):
+    """
+    Demonstrate stochastic gradient descent optimization for a multilayer 
+    perceptron
+
+    This is demonstrated on MNIST.
+
+    :param learning_rate: learning rate used (factor for the stochastic 
+    gradient
+
+    :param n_iter: number of iterations ot run the optimizer 
+
+    :param L1_reg: L1-norm's weight when added to the cost (see 
+    regularization)
+
+    :param L2_reg: L2-norm's weight when added to the cost (see 
+    regularization)
+    """
+
+    # 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
+
+    # 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 = MLP( input=x.reshape((batch_size,28*28)),\
+                      n_in=28*28, n_hidden = 500, n_out=10)
+
+    # the cost we minimize during training is the negative log likelihood of 
+    # the model plus the regularization terms (L1 and L2); cost is expressed
+    # here symbolically
+    cost = classifier.negative_log_likelihood(y) \
+         + L1_reg * classifier.L1 \
+         + L2_reg * classifier.L2_sqr 
+
+    # compiling 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))
+
+    # compute the gradient of cost with respect to theta = (W1, b1, W2, b2) 
+    g_W1 = T.grad(cost, classifier.W1)
+    g_b1 = T.grad(cost, classifier.b1)
+    g_W2 = T.grad(cost, classifier.W2)
+    g_b2 = T.grad(cost, classifier.b2)
+
+    # specify how to update the parameters of the model as a dictionary
+    updates = \
+        { classifier.W1: classifier.W1 - learning_rate*g_W1 \
+        , classifier.b1: classifier.b1 - learning_rate*g_b1 \
+        , classifier.W2: classifier.W2 - learning_rate*g_W2 \
+        , classifier.b2: classifier.b2 - learning_rate*g_b2 }
+
+    # 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([x, y], cost, updates = updates )
+    n_minibatches        = len(train_batches) 
+ 
+    # early-stopping parameters
+    patience              = 10000 # 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  = n_minibatches  # go through this many 
+                                  # minibatche before checking the network 
+                                  # on the validation set; in this case we 
+                                  # check every epoch 
+
+
+    best_params          = None
+    best_validation_loss = float('inf')
+    test_score           = 0.
+    start_time = time.clock()
+    # have a maximum of `n_iter` iterations through the entire dataset
+    for iter in xrange(n_iter* n_minibatches):
+
+        # get epoch and minibatch index
+        epoch           = iter / n_minibatches
+        minibatch_index =  iter % n_minibatches
+
+        # get the minibatches corresponding to `iter` modulo
+        # `len(train_batches)`
+        x,y = train_batches[ minibatch_index ]
+        cost_ij = train_model(x,y)
+
+        if (iter+1) % validation_frequency == 0: 
+            # compute zero-one loss on validation set 
+            this_validation_loss = 0.
+            for x,y in valid_batches:
+                # sum up the errors for each minibatch
+                this_validation_loss += test_model(x,y)
+            # get the average by dividing with the number of minibatches
+            this_validation_loss /= len(valid_batches)
+
+            print('epoch %i, minibatch %i/%i, validation error %f %%' % \
+                   (epoch, minibatch_index+1, n_minibatches, \
+                    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_score = 0.
+                for x,y in test_batches:
+                    test_score += test_model(x,y)
+                test_score /= len(test_batches)
+                print(('     epoch %i, minibatch %i/%i, test error of best '
+                      'model %f %%') % 
+                             (epoch, minibatch_index+1, n_minibatches,
+                              test_score*100.))
+
+        if patience <= iter :
+                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 ran for %f minutes' % ((end_time-start_time)/60.))
+
+
+
+
+
+
+if __name__ == '__main__':
+    sgd_optimization_mnist()
+