function [theta, ll] = logistic_grad_ascent(X,y)

% rows of X are training samples
% rows of Y are corresponding 0/1 values

% output ll: vector of log-likelihood values at each iteration
% ouptut theta: parameters

alpha = 0.0001;

m = size(X, 1);
n = size(X, 2);

max_iters = 500;

X = [ones(size(X,1)), X]; % append col of ones for intercept term

theta = zeros(n, 1);  % initialize theta
for k = 1:max_iters
  
  hx = sigmoid(X*theta);
  theta = theta + alpha * X' * (Y-hx)); 
  ll(k) = sum( Y .* log(hx) + (1 - Y) .* log(1 - hx) ); 
  
end