Logistic Regression Gradient Descent in Matlab

Question

Here is the code

function [theta] = LR(D)
% D is the data having feature variables and class labels

% Now decompose D into X and C 
%Note that dimensions of X =  , C = 

C = D(:,1);
C = C';
size(C)
X = D(:,2:size(D,2));
size(X)
alpha = .00001;

theta_old = zeros(1,34);
theta_new = .001.*ones(1,34);
count = 1;
for count = 1:100000
    theta_old = theta_new;
    theta_new = theta_new + alpha*(C-sigmoid(X*theta_new')')*X;
    llr =  sum(LLR((X*theta_new').*(C'))) 
end
thetaopt = theta_new


end


function a = LLR( z )
a= 1.*log(1.0 + exp(-z));
end

function a = sigmoid(z)
 a = 1.0 ./ (1.0 + exp(-z));
 end

The problem I have is that the log likelihood ratio first decreases, and then starts increasing. Is this a problem with the Gradient Descent algorithm or with the code.

Answer 1

It looks like there could be a problem with your objective function.

If the labels (C) are in {0,1}, then you should be using the loss C.*LLR(X*theta')+(1-C).*(LLR(X*theta')+X*theta')

If your labels are in {-1,1}, then the loss should be LLR(C.*X*theta').

You seem to be using only the first part of the first type of loss function.