Theano深度学习教程Python代码

.. _gettingstarted: =============== Getting Started =============== These tutorials do not attempt to make up for a graduate or undergraduate course in machine learning, but we do make a rapid overview of some important concepts (and notation) to make sure that we're on the same page. You'll also need to download the datasets mentioned in this chapter in order to run the example code of the up-coming tutorials. .. _download: .. index:: Download: Download ======== On each learning algorithm page, you will be able to download the corresponding files. If you want to download all of them at the same time, you can clone the git repository of the tutorial:: git clone https://github.com/lisa-lab/DeepLearningTutorials.git .. _datasets: .. index:: Datasets Datasets ======== .. index:: MNIST Dataset MNIST Dataset +++++++++++++ (`mnist.pkl.gz <http://deeplearning.net/data/mnist/mnist.pkl.gz>`_) The `MNIST <http://yann.lecun.com/exdb/mnist>`_ dataset consists of handwritten digit images and it is divided in 60,000 examples for the training set and 10,000 examples for testing. In many papers as well as in this tutorial, the official training set of 60,000 is divided into an actual training set of 50,000 examples and 10,000 validation examples (for selecting hyper-parameters like learning rate and size of the model). All digit images have been size-normalized and centered in a fixed size image of 28 x 28 pixels. In the original dataset each pixel of the image is represented by a value between 0 and 255, where 0 is black, 255 is white and anything in between is a different shade of grey. Here are some examples of MNIST digits: |0| |1| |2| |3| |4| |5| .. |0| image:: images/mnist_0.png .. |1| image:: images/mnist_1.png .. |2| image:: images/mnist_2.png .. |3| image:: images/mnist_3.png .. |4| image:: images/mnist_4.png .. |5| image:: images/mnist_5.png For convenience we pickled the dataset to make it easier to use in python. It is available for download `here <http://deeplearning.net/data/mnist/mnist.pkl.gz>`_. The pickled file represents a tuple of 3 lists : the training set, the validation set and the testing set. Each of the three lists is a pair formed from a list of images and a list of class labels for each of the images. An image is represented as numpy 1-dimensional array of 784 (28 x 28) float values between 0 and 1 (0 stands for black, 1 for white). The labels are numbers between 0 and 9 indicating which digit the image represents. The code block below shows how to load the dataset. .. code-block:: python import cPickle, gzip, numpy # Load the dataset f = gzip.open('mnist.pkl.gz', 'rb') train_set, valid_set, test_set = cPickle.load(f) f.close() When using the dataset, we usually divide it in minibatches (see :ref:`opt_SGD`). We encourage you to store the dataset into shared variables and access it based on the minibatch index, given a fixed and known batch size. The reason behind shared variables is related to using the GPU. There is a large overhead when copying data into the GPU memory. If you would copy data on request ( each minibatch individually when needed) as the code will do if you do not use shared variables, due to this overhead, the GPU code will not be much faster then the CPU code (maybe even slower). If you have your data in Theano shared variables though, you give Theano the possibility to copy the entire data on the GPU in a single call when the shared variables are constructed. Afterwards the GPU can access any minibatch by taking a slice from this shared variables, without needing to copy any information from the CPU memory and therefore bypassing the overhead. Because the datapoints and their labels are usually of different nature (labels are usually integers while datapoints are real numbers) we suggest to use different variables for label and data. Also we recommend using different variables for the training set, validation set and testing set to make the code more readable (resulting in 6 different shared variables). Since now the data is in one variable, and a minibatch is defined as a slice of that variable, it comes more natural to define a minibatch by indicating its index and its size. In our setup the batch size stays constant throughout the execution of the code, therefore a function will actually require only the index to identify on which datapoints to work. The code below shows how to store your data and how to access a minibatch: .. code-block:: python 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 us 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 = 500 # size of the minibatch # accessing the third minibatch of the training set data = train_set_x[2 * batch_size: 3 * batch_size] label = train_set_y[2 * batch_size: 3 * batch_size] The data has to be stored as floats on the GPU ( the right ``dtype`` for storing on the GPU is given by ``theano.config.floatX``). To get around this shortcomming for the labels, we store them as float, and then cast it to int. .. note:: If you are running your code on the GPU and the dataset you are using is too large to fit in memory the code will crash. In such a case you should store the data in a shared variable. You can however store a sufficiently small chunk of your data (several minibatches) in a shared variable and use that during training. Once you got through the chunk, update the values it stores. This way you minimize the number of data transfers between CPU memory and GPU memory. .. index:: Notation Notation ======== .. index:: Dataset notation Dataset notation ++++++++++++++++ We label data sets as :math:`\mathcal{D}`. When the distinction is important, we indicate train, validation, and test sets as: :math:`\mathcal{D}_{train}`, :math:`\mathcal{D}_{valid}` and :math:`\mathcal{D}_{test}`. The validation set is used to perform model selection and hyper-parameter selection, whereas the test set is used to evaluate the final generalization error and compare different algorithms in an unbiased way. The tutorials mostly deal with classification problems, where each data set :math:`\mathcal{D}` is an indexed set of pairs :math:`(x^{(i)},y^{(i)})`. We use superscripts to distinguish training set examples: :math:`x^{(i)} \in \mathcal{R}^D` is thus the i-th training example of dimensionality :math:`D`. Similarly, :math:`y^{(i)} \in \{0, ..., L\}` is the i-th label assigned to input :math:`x^{(i)}`. It is straightforward to extend these examples to ones where :math:`y^{(i)}` has other types (e.g. Gaussian for regression, or groups of multinomials for predicting multiple