.. _logistic_regression_example:

State example
=============

In this example, we'll look at a complete logistic regression model, with
training by gradient descent.

BUT, YOU GOTTA RUN THIS CODE AND MAKE SURE IT STILL WORKS NICELY, HEY?

.. code-block:: python

    def build_logistic_regression_model(n_in, n_out, l2_coef=30.0)
        # DECLARE SOME VARIABLES

        import tensor as at

        x = at.matrix()  #our points, one point per row
        y = at.matrix()  #store our labels as place codes (label 3 of 5 is vector [00100])

        w = at.matrix()  #the linear transform to apply to our input points
        b = at.vector()  #a vector of biases, which make our transform affine instead of linear

        stepsize = at.scalar('stepsize')  # a stepsize for gradient descent

        # REGRESSION MODEL AND COSTS TO MINIMIZE

        prediction = at.softmax(at.dot(x, w) + b)
        cross_entropy = at.sum(y * at.log(prediction), axis=1)
        cost = at.sum(cross_entropy) + l2_coef * at.sum(at.sum(w*w))

        # GET THE GRADIENTS NECESSARY TO FIT OUR PARAMETERS

        grad_w, grad_b = at.grad(cost, [w, b])

        #
        # GET THE GRADIENTS NECESSARY TO FIT OUR PARAMETERS

        update_fn = pytensor.function(
            inputs = [x, y, stepsize,
                In(w,
                    name='w',
                    value=numpy.zeros((n_in, n_out)),
                    update=w - stepsize * grad_w,
                    mutable=True,
                    strict=True)
                In(b,
                    name='b',
                    value=numpy.zeros(n_out),
                    update=b - lr * grad_b,
                    mutable=True,
                    strict=True)
            ],
            outputs = cost,
            mode = 'EXPENSIVE_OPTIMIZATIONS')

        apply_fn = pytensor.function(
            inputs = [x, In(w, value=update_fn.storage[w]), In(b, value=update_fn.storage[b])],
            outputs = [prediction])

        return update_fn, apply_fn

    #USUALLY THIS WOULD BE IN A DIFFERENT FUNCTION/CLASS
    #FIT SOME DUMMY DATA: 100 points with 10 attributes and 3 potential labels

    up_fn, app_fn = build_logistic_regression_model(n_in=10, n_out=3, l2_coef=30.0)

    x_data = numpy.random.standard_normal((100, 10))
    y_data = numpy.random.standard_normal((100, 3))
    y_data = _asarray(y_data == numpy.max(y_data, axis=1), dtype='int64')

    print "Model Training ..."
    for iteration in range(1000):
        print "  iter", iteration, "cost", update_fn(x_data, y_data, stepsize=0.0001)

    print "Model Predictions"
    print apply_fn(x_data)
