def evaluate_lenet5(initial_learning_rate=0.1, learning_rate_decay = 1, dropout_rates = [0.2, 0.2, 0.2, 0.5], n_epochs=200,
                    dataset='mnist.pkl.gz',
                    nkerns=[20, 50], batch_size=500):
    """ Demonstrates lenet on MNIST dataset

    :type learning_rate: float
    :param learning_rate: learning rate used (factor for the stochastic
                          gradient)

    :type learning_rate_decay: float
    :param learning_rate_decay: learning rate decay used (1 means learning rate decay is deactivated)

    :type dropout_rates: list of float
    :param dropout_rates: dropout rate used for each layer (input layer, 1st filtered layer, 2nd filtered layer, fully connected layer)

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

    :type dataset: string
    :param dataset: path to the dataset used for training /testing (MNIST here)

    :type nkerns: list of ints
    :param nkerns: number of kernels on each layer
    """

    rng = numpy.random.RandomState(23455)

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

    # allocate symbolic variables for the data
    index = T.lscalar()  # index to a [mini]batch
    epoch = T.scalar()

    x = T.matrix('x')   # the data is presented as rasterized images
    y = T.ivector('y')  # the labels are presented as 1D vector of
                        # [int] labels

    learning_rate = theano.shared(numpy.asarray(initial_learning_rate,
        dtype=theano.config.floatX))

    ######################
    # BUILD ACTUAL MODEL #
    ######################
    print '... building the model'

    # Reshape matrix of rasterized images of shape (batch_size, 28 * 28)
    # to a 4D tensor, compatible with our LeNetConvPoolLayer
    # (28, 28) is the size of MNIST images.
    layer0_input = x.reshape((batch_size, 1, 28, 28))
    layer0_input_dropout = _dropout_from_layer(rng, layer0_input, dropout_rates[0])


    # Construct the first convolutional pooling layer:
    # filtering reduces the image size to (28-5+1 , 28-5+1) = (24, 24)
    # maxpooling reduces this further to (24/2, 24/2) = (12, 12)
    # 4D output tensor is thus of shape (batch_size, nkerns[0], 12, 12)
    layer0_dropout = DropoutLeNetConvPoolLayer(
        rng,
        input=layer0_input_dropout,
        image_shape=(batch_size, 1, 28, 28),
        filter_shape=(nkerns[0], 1, 5, 5),
        poolsize=(2, 2),
        dropout_rate= dropout_rates[1]
    )

    layer0 = LeNetConvPoolLayer(
      rng,
      input=layer0_input,
      image_shape=(batch_size, 1, 28, 28),
      filter_shape=(nkerns[0], 1, 5, 5),
      poolsize=(2, 2),
      W=layer0_dropout.W * (1 - dropout_rates[0]),
      b=layer0_dropout.b
    )

    # Construct the second convolutional pooling layer
    # filtering reduces the image size to (12-5+1, 12-5+1) = (8, 8)
    # maxpooling reduces this further to (8/2, 8/2) = (4, 4)
    # 4D output tensor is thus of shape (batch_size, nkerns[1], 4, 4)
    layer1_dropout = DropoutLeNetConvPoolLayer(
        rng,
        input=layer0_dropout.output,
        image_shape=(batch_size, nkerns[0], 12, 12),
        filter_shape=(nkerns[1], nkerns[0], 5, 5),
        poolsize=(2, 2),
        dropout_rate = dropout_rates[2]
    )

    layer1 = LeNetConvPoolLayer(
      rng,
      input=layer0.output,
      image_shape=(batch_size, nkerns[0], 12, 12),
      filter_shape=(nkerns[1], nkerns[0], 5, 5),
      poolsize=(2, 2),
      W=layer1_dropout.W * (1 - dropout_rates[1]),
      b=layer1_dropout.b
    )

    # the HiddenLayer being fully-connected, it operates on 2D matrices of
    # shape (batch_size, num_pixels) (i.e matrix of rasterized images).
    # This will generate a matrix of shape (batch_size, nkerns[1] * 4 * 4),
    # or (500, 50 * 4 * 4) = (500, 800) with the default values.
    layer2_dropout_input = layer1_dropout.output.flatten(2)
    layer2_input = layer1.output.flatten(2)

    # construct a fully-connected sigmoidal layer
    layer2_dropout = DropoutHiddenLayer(
        rng,
        input=layer2_dropout_input,
        n_in=nkerns[1] * 4 * 4,
        n_out=500,
        activation=T.tanh,
        dropout_rate = dropout_rates[3]
    )

    layer2 = HiddenLayer(
      rng,
      input=layer2_input,
      n_in=nkerns[1] * 4 * 4,
      n_out=500,
      activation=T.tanh,
      W=layer2_dropout.W * (1 - dropout_rates[2]),
      b=layer2_dropout.b
    )


    # classify the values of the fully-connected sigmoidal layer
    layer3_dropout = LogisticRegression(
      input = layer2_dropout.output,
      n_in = 500, n_out = 10)

    layer3 = LogisticRegression(
      input=layer2.output,
      n_in=500, n_out=10,
      W=layer3_dropout.W * (1 - dropout_rates[-1]),
      b=layer3_dropout.b
    )


    # the cost we minimize during training is the NLL of the model
    cost = layer3.negative_log_likelihood(y)
    dropout_cost = layer3_dropout.negative_log_likelihood(y)

    # create a function to compute the mistakes that are made by the model
    test_model = theano.function(
        [index],
        layer3.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(
        [index],
        layer3.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]
        }
    )

    # create a list of all model parameters to be fit by gradient descent
    params = layer3_dropout.params + layer2_dropout.params + layer1_dropout.params + layer0_dropout.params

    # create a list of gradients for all model parameters
    grads = T.grad(dropout_cost, params)

    # train_model is a function that updates the model parameters by
    # SGD Since this model has many parameters, it would be tedious to
    # manually create an update rule for each model parameter. We thus
    # create the updates list by automatically looping over all
    # (params[i], grads[i]) pairs.
    updates = [
        (param_i, param_i - learning_rate * grad_i)
        for param_i, grad_i in zip(params, grads)
    ]

    train_model = theano.function(
        [index],
        dropout_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]
        }
    )

    # Theano function to decay the learning rate
    decay_learning_rate = theano.function(inputs=[], outputs=learning_rate,
            updates={learning_rate: learning_rate * learning_rate_decay})

    ###############
    # TRAIN MODEL #
    ###############
    print '... training'
    # 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 = 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 = numpy.inf
    best_iter = 0
    test_score = 0.
    start_time = timeit.default_timer()

    epoch = 0
    done_looping = False

    while (epoch < n_epochs) and (not done_looping):
        epoch = epoch + 1
        for minibatch_index in xrange(n_train_batches):

            iter = (epoch - 1) * n_train_batches + minibatch_index

            if iter % 100 == 0:
                print 'training @ iter = ', iter
            cost_ij = train_model(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 = numpy.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)

                    # save best validation score and iteration number
                    best_validation_loss = this_validation_loss
                    best_iter = iter

                    # test it on the test set
                    test_losses = [
                        test_model(i)
                        for i in xrange(n_test_batches)
                    ]
                    test_score = numpy.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
        new_learning_rate = decay_learning_rate()

    end_time = timeit.default_timer()
    print('Optimization complete.')
    print('Best validation score of %f %% obtained at iteration %i, '
          'with test performance %f %%' %
          (best_validation_loss * 100., best_iter + 1, test_score * 100.))
    print >> sys.stderr, ('The code for file ' +
                          os.path.split(__file__)[1] +
                          ' ran for %.2fm' % ((end_time - start_time) / 60.))
  def __init__(self,
               rng,
               input,
               filter_shapes,
               image_shape,
               poolsize,
               layer_sizes,
               dropout_rates,
               activations):

    """
    Allocate a cnn_mlp (ConvNet followed by MLP) with shared variable internal parameters.

    :type rng: numpy.random.RandomState
    :param rng: a random number generator used to initialize weights

    :type input: theano.tensor.dtensor4
    :param input: symbolic image tensor, of shape image_shape

    :type filter_shapes:  list of (list of length 4)
    :param filter_shapes: list of the filters whith their respective properties ((number of kernels, num input feature maps,
                                                                                  filter height, filter width), ...)
                          len(filter_shapes) = number of LeNetConvPoolLayer layers

    :type image_shape: tuple or list of length 4
    :param image_shape: (batch size, num input feature maps,
                             image height, image width)

    :type poolsize: tuple or list of length 2
    :param poolsize: the downsampling (pooling) factor (#rows, #cols)

    :type layer_sizes: list of int
    :param layer_sizes: sizes (number of units) of each HiddenLayer (
                        len(layer_sizes) = number of HiddenLayer layers)

    :type dropout_rates: list of float
    :param dropout_rates: dropout rate used for each layer (including dropout on the input)

    :type activations: list of theano.function
    :param activations: list of the activation functions to use at each layer

    """


    #######################################
    # Set up all the convolutional layers #
    #######################################

    self.layers = []
    self.dropout_layers = []

    next_layer_input = input.reshape(image_shape)
    next_dropout_layer_input = _dropout_from_layer(rng, next_layer_input, p=dropout_rates[0])

    layer_counter = 0

    for i in range(len(filter_shapes)):

      filter_shape = filter_shapes[i]

      next_dropout_layer = DropoutLeNetConvPoolLayer(
        rng=rng,
        input=next_dropout_layer_input,
        image_shape=image_shape,
        filter_shape=filter_shape,
        poolsize=poolsize,
        dropout_rate=dropout_rates[layer_counter + 1],
        activation=activations[layer_counter]
        )

      self.dropout_layers.append(next_dropout_layer)
      next_dropout_layer_input = next_dropout_layer.output

      # Reuse parameters from the dropout layer here
      next_layer = LeNetConvPoolLayer(
        rng=rng,
        input=next_layer_input,
        image_shape=image_shape,
        filter_shape=filter_shape,
        W=next_dropout_layer.W * (1 - dropout_rates[layer_counter]),
        b=next_dropout_layer.b,
        poolsize=poolsize,
        activation=activations[layer_counter]
        )

      self.layers.append(next_layer)
      next_layer_input = next_layer.output

      image_shape = (image_shape[0],
                     filter_shape[0],
                     (image_shape[2] - filter_shape[2] + 1) / poolsize[0],
                     (image_shape[3] - filter_shape[3] + 1) / poolsize[1])

      layer_counter += 1

    ################################
    # Set up all the hidden layers #
    ################################

    weight_matrix_sizes = zip(layer_sizes, layer_sizes[1:])

    next_layer_input = next_layer_input.flatten(2)
    next_dropout_layer_input = next_dropout_layer_input.flatten(2)

    assert (layer_sizes[0] == numpy.prod(image_shape[1:])), "The dimension of the first hidden layer does not match last convolutional layer size."

    for n_in, n_out in weight_matrix_sizes[:-1]:

      next_dropout_layer = DropoutHiddenLayer(
        rng=rng,
        input=next_dropout_layer_input,
        activation=activations[layer_counter],
        n_in=n_in,
        n_out=n_out,
        dropout_rate=dropout_rates[layer_counter + 1])

      self.dropout_layers.append(next_dropout_layer)
      next_dropout_layer_input = next_dropout_layer.output

      # Reuse the paramters from the dropout layer here
      next_layer = HiddenLayer(
        rng=rng,
        input=next_layer_input,
        activation=activations[layer_counter],
        # scale the weight matrix W with (1-p)
        W=next_dropout_layer.W * (1 - dropout_rates[layer_counter]),
        b=next_dropout_layer.b,
        n_in=n_in,
        n_out=n_out)

      self.layers.append(next_layer)
      next_layer_input = next_layer.output

      layer_counter += 1

    ###########################
    # Set up the output layer #
    ###########################

    n_in, n_out = weight_matrix_sizes[-1]

    dropout_output_layer = LogisticRegression(
      input=next_dropout_layer_input,
      n_in=n_in,
      n_out=n_out)
    self.dropout_layers.append(dropout_output_layer)

    # Again, reuse paramters in the dropout output.
    output_layer = LogisticRegression(
      input=next_layer_input,
      # scale the weight matrix W with (1-p)
      W=dropout_output_layer.W * (1 - dropout_rates[-1]),
      b=dropout_output_layer.b,
      n_in=n_in,
      n_out=n_out)
    self.layers.append(output_layer)

    # Use the negative log likelihood of the logistic regression layer as
    # the objective.
    self.dropout_negative_log_likelihood = self.dropout_layers[-1].negative_log_likelihood
    self.dropout_errors = self.dropout_layers[-1].errors

    self.negative_log_likelihood = self.layers[-1].negative_log_likelihood
    self.errors = self.layers[-1].errors

    # Grab all the parameters together.
    self.params = [ param for layer in self.dropout_layers for param in layer.params ]