Logistic prediction

log_regression.py

def sigmoid(X):
    '''Compute the sigmoid function '''
    #d = zeros(shape=(X.shape))

    den = 1.0 + e ** (-1.0 * X)

    d = 1.0 / den

    return d


def compute_cost(theta,X,y): #computes cost given predicted and actual values
    m = X.shape[0] #number of training examples
    theta = reshape(theta,(len(theta),1))

    #y = reshape(y,(len(y),1))
    
    J = (1./m) * (-transpose(y).dot(log(sigmoid(X.dot(theta)))) - transpose(1-y).dot(log(1-sigmoid(X.dot(theta)))))
    
    grad = transpose((1./m)*transpose(sigmoid(X.dot(theta)) - y).dot(X))
    #optimize.fmin expects a single value, so cannot return grad
    return J[0][0]#,grad


def compute_grad(theta, X, y):

    #print theta.shape

    theta.shape = (1, 3)

    grad = zeros(3)

    h = sigmoid(X.dot(theta.T))

    delta = h - y

    l = grad.size

    for i in range(l):
        sumdelta = delta.T.dot(X[:, i])
        grad[i] = (1.0 / m) * sumdelta * - 1

    theta.shape = (3,)

    return  grad

@cipri-tom scaled by y.size to calculate the average since summed over all training data I think

I think your code is not converging to the minimum. As I tested is not converging at all. Check this tutorial code that I'll post below here and I think it will make sense. Your full code, that is not this one is converging to the initial parameter vector, which is (0,0,0). Try using fmin_tnc instead of fmin_bfgs.
Btw, excellent work.

http://www.johnwittenauer.net/machine-learning-exercises-in-python-part-3/