Linear Regression with Theano - Dimension Mis-match

Question

I am familiarizing myself with Theano and machine learning. To that end, I'd like to calculate a linear regression. My code is inspired by the logistic regression example from the introduction to Theano.

I wrote the following code:

    import numpy
    import theano
    import theano.tensor as T

    class LinearRegression(object):
        """ Calculate Linear Regression """

        def __init__(self, input):
            """ Initialize the parameters of the logistic regression

            Parameters:
            -----------

            :type input: theano.tensor.TensorType
            :param input: symbolic variable that describes the input of the
                          architecture (one minibatch)
            """
            self.W = theano.shared(
                value=numpy.zeros(1, dtype=theano.config.floatX),
                name='W', borrow=True
            )

            self.b = theano.shared(
                value=numpy.zeros(1, dtype=theano.config.floatX),
                name='b', borrow=True
            )

            self.y_pred = T.dot(input, self.W) + self.b

        def errors(self, y):
            """ The squared distance

            Parameters:
            ----------

            :y input: array_like:
            :param input: the sample data

            """
            errors = y- self.y_pred
            return T.sum(T.pow(errors, 2))


    def sgd_optimization(learning_rate=0.0013, n_epochs=100):
        """
        Demonstrate stochastic gradient descent optimization of a linear model

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

        :type n_epochs: int
        :param n_epochs: maximal number of epochs to run the optimizer
        """
        x_train = numpy.random.uniform(low=-2, high = 2, size=(50,1))
        epsilon =  numpy.random.normal(scale=0.01, size=50)
        y_train = numpy.squeeze(2*x_train) + epsilon

        costs = []
        eta0, x, y = T.scalar('eta0'), T.matrix(name='x'), T.vector(name='y')

        classifier = LinearRegression(input = x)
        cost = classifier.errors(y)
        g_W = T.grad(cost=cost, wrt=classifier.W)
        g_b = T.grad(cost=cost, wrt=classifier.b)
        update = [(classifier.W, classifier.W - eta0 * g_W),
                   (classifier.b, classifier.b - eta0 * g_b)]

        train = theano.function(inputs = [eta0],
                                outputs = cost,
                                updates = update,
                                givens = {x: x_train, y: y_train})

        for _ in range(n_epochs):
            costs.append(train(learning_rate))

        return costs, w

    SSE, regressor = sgd_optimization()

Unfortunately, Python returns the following error message when I run the code:

ValueError: Input dimension mis-match. (input[0].shape[0] = 1, input[1].shape[0] = 50)
Apply node that caused the error: Elemwise{Composite{((-i0) + i1)}}[(0, 1)](b, CGemv{no_inplace}.0)
Inputs types: [TensorType(float64, vector), TensorType(float64, vector)]
Inputs shapes: [(1,), (50,)]
Inputs strides: [(8,), (8,)]
Inputs values: [array([ 0.]), 'not shown']

HINT: Re-running with most Theano optimization disabled could give you a back-trace of when this node was created. This can be done with by setting the Theano flag 'optimizer=fast_compile'. If that does not work, Theano optimizations can be disabled with 'optimizer=None'.
HINT: Use the Theano flag 'exception_verbosity=high' for a debugprint and storage map footprint of this apply node.

I suspect the error is related to the sample data being of dimension (50,1) and the regressor only of dimension of (1,1). Nevertheless, I failed to correct the error in my code since some time. Can somebody provide a hint for how to correct the mistake? I'm grateful for any help!

Answer 1

You need to broadcast b :

self.y_pred = T.dot(input, self.W) + self.b[:, None]

I would expect Theano to do this automatically, but it seems this is not the case.

---

To locate the problem follow the error message suggestion and run Theano with high exception verbosity

$ THEANO_FLAGS='exception_verbosity=high' python path/to/script.py

This produces quite a lot of output including the problematic node along with its operands

Debugprint of the apply node:
Elemwise{Composite{((-i0) + i1)}}[(0, 1)] [@A] <TensorType(float64, vector)> ''
 |b [@B] <TensorType(float64, vector)>
 |CGemv{no_inplace} [@C] <TensorType(float64, vector)> ''
   |<TensorType(float64, vector)> [@D] <TensorType(float64, vector)>
   |TensorConstant{-1.0} [@E] <TensorType(float64, scalar)>
   |<TensorType(float64, matrix)> [@F] <TensorType(float64, matrix)>
   |W [@G] <TensorType(float64, vector)>
   |TensorConstant{1.0} [@H] <TensorType(float64, scalar)>

The node corresponds to a subtraction of b from a temporary node CGemv{no_inplace} . The only line of code involving b is

self.y_pred = T.dot(input, self.W) + self.b