Vectorized Regularized Gradient Descent not passing numerical check

Question

I've written an implementation in Python using NumPy of vectorized regularized Gradient descent for logistic regression. I've used a numerical check method to check that my implementation is correct. The numerical check verifies my implementation of Linear regression GD, but Logisitc fails, and I cannot find out. Any help would be appreciated. So here goes:

Those are my methods for calculating cost and gradient (update function calculates gradient and updates the parameters):

@staticmethod
def _hypothesis(parameters, features):
    return Activation.sigmoid(features.dot(parameters))

@staticmethod
def _cost_function(parameters, features, targets):
    m = features.shape[0]
    return np.sum(-targets * (np.log(LogisticRegression._hypothesis(parameters, features)) - (1 - targets) * (
        np.log(1 - LogisticRegression._hypothesis(parameters, features))))) / m

@staticmethod
def _update_function(parameters, features, targets, extra_param):
    regularization_vector = extra_param.get("regularization_vector", 0)
    alpha = extra_param.get("alpha", 0.001)
    m = features.shape[0]

    return parameters - alpha / m * (
        features.T.dot(LogisticRegression._hypothesis(parameters, features) - targets)) + \
           (regularization_vector / m) * parameters

The cost function doesn't have regularization included, but the test I do is with a regularization vector equal to zero so it does not matter. How I am testing:

def numerical_check(features, parameters, targets, cost_function, update_function, extra_param, delta):
gradients = - update_function(parameters, features, targets, extra_param)

parameters_minus = np.copy(parameters)
parameters_plus = np.copy(parameters)
parameters_minus[0, 0] = parameters_minus[0, 0] + delta
parameters_plus[0, 0] = parameters_plus[0, 0] - delta

approximate_gradient = - (cost_function(parameters_plus, features, targets) -
                          cost_function(parameters_minus, features, targets)) / (2 * delta) / parameters.shape[0]

return abs(gradients[0, 0] - approximate_gradient) <= delta

Basically, I am manually calculating the gradient when I shift the first parameter delta amount to the left and to the right. And then I compare it with the gradients I get from the update function. I am using initial parameters equal to 0 so the updated parameter received is equal to the gradient divided by and the number of features. Also alpha is equal to one. Unfortunately, I am getting different values from the two methods and I cannot find out why. Any advice on how to troubleshoot this problem would be really appreciated.

Answer 1

there is an error in your cost function. error is due to invalid distribution of brackets. i've fixed that

def _cost_function(parameters, features, targets):
    m = features.shape[0]
    
    return -np.sum(
        (    targets) * (np.log(    LogisticRegression._hypothesis(parameters, features)))
      + (1 - targets) * (np.log(1 - LogisticRegression._hypothesis(parameters, features)))
    ) / m

try writing your code cleanly, it helps to detect errors like these