cost function for the logistic regression in matlab

The cost function for logistic regression in Matlab is given by:

main.m
function [J, grad] = costFunction(theta, X, y)
m = length(y); % number of training examples
J = 0;
grad = zeros(size(theta));
hypothesis = sigmoid(X * theta);
J = (-y' * log(hypothesis) - (1-y)' * log(1-hypothesis)) / m;
grad = X' * (hypothesis - y) / m;
end
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This function takes in the parameters theta (the weights), feature matrix X, and target values y as input and returns the cost function value J and the gradient of J with respect to theta.

The cost function J is calculated using the sigmoid function to make predictions based on the input features and the current parameter values of theta. The resulting predictions are compared to the ground truth labels y, and the average sum of error over all the training examples is returned as J.

The gradient of the cost function is also calculated using the feature matrix X and the difference between predictions and ground truth labels y. The gradient is then used to update the parameter values to minimize J, by using an optimization algorithm such as gradient descent.

In summary, the cost function for logistic regression in Matlab is used to measure the accuracy of a machine learning model, and the gradient descent algorithm uses this function to optimize the parameters of the model to make better predictions on new data.