logistic_train.m

function [weights] = logistic_train(data, labels, epsilon, maxiter)
%
% code to train a logistic regression classifier
%
% INPUTS:
%  data   = n * (d+1) matrix withn samples and d features, where
%          column d+1 is all ones (corresponding to the intercept term)
%  labels = n * 1 vector of class labels (taking values 0 or 1)
% epsilon = optional argument specifying the convergence
%           criterion - if the change in the absolute difference in
%           predictions, from one iteration to the next, averaged across
%           input features, is less than epsilon, then halt
%           (if unspecified, use a default value of 1e-5)
% maxiter = optional argument that specifies the maximum number of
%           iterations to execute (useful when debugging in case your
%           code is not converging correctly!)
%           (if unspecified can be set to 1000)
%
% OUTPUT:
% weights = (d+1) * 1 vector of weights where the weights correspond to
%           the columns of "data"
%

% read parameters
if nargin < 2
    fprintf('Need at least two parameters!');
    return;
end
if nargin < 3
    epsilon = 1e-5;
end
if nargin < 4
    maxiter = 1000;
end

n = size(data,2);
% initialize weights
weights_t = zeros(n,1);
y_t = logsig(data*weights_t);
iter = 0;
% using Newton-Raphson (IRLS) iterative procedure
while iter < maxiter
    % avoid the issue y(1-y) become 0, which lead to sigular matrix H
    if sum(y_t==0)>0 || sum(y_t==1)>0
        break;
    end
    R = diag(y_t.*(1-y_t));
    dE = data'*(y_t-labels);
    H = data'*R*data;
    weights = weights_t-H\dE;
    y = logsig(data*weights);
    % convergence criterion
    if mean(abs(y-y_t)) < epsilon
        break;
    end
    y_t = y;
    weights_t = weights;
    iter = iter+1;
end

end