Regularized logistic regression code in matlab

Question

I'm trying my hand at regularized LR, simple with this formulas in matlab:

The cost function:

J(theta) = 1/m*sum((-y_i)*log(h(x_i)-(1-y_i)*log(1-h(x_i))))+(lambda/2*m)*sum(theta_j)

The gradient:

∂J(theta)/∂theta_0 = [(1/m)*(sum((h(x_i)-y_i)*x_j)] if j=0

∂j(theta)/∂theta_n = [(1/m)*(sum((h(x_i)-y_i)*x_j)]+(lambda/m)*(theta_j) if j>1

This is not matlab code is just the formula.

So far I've done this:

function [J, grad] = costFunctionReg(theta, X, y, lambda)

J = 0;
grad = zeros(size(theta));

temp_theta = [];

%cost function

%get the regularization term

for jj = 2:length(theta)

    temp_theta(jj) = theta(jj)^2;
end

theta_reg = lambda/(2*m)*sum(temp_theta);

temp_sum =[];

%for the sum in the cost function

for ii =1:m

   temp_sum(ii) = -y(ii)*log(sigmoid(theta'*X(ii,:)'))-(1-y(ii))*log(1-sigmoid(theta'*X(ii,:)'));

end

tempo = sum(temp_sum);

J = (1/m)*tempo+theta_reg;

%regulatization
%theta 0

reg_theta0 = 0;

for jj=1:m
 reg_theta0(jj) = (sigmoid(theta'*X(m,:)') -y(jj))*X(jj,1)
end    

reg_theta0 = (1/m)*sum(reg_theta0)

grad_temp(1) = reg_theta0

%for the rest of thetas

reg_theta  = [];
thetas_sum = 0;

for ii=2:size(theta)
    for kk =1:m
        reg_theta(kk) = (sigmoid(theta'*X(m,:)') - y(kk))*X(kk,ii)
    end
    thetas_sum(ii) = (1/m)*sum(reg_theta)+(lambda/m)*theta(ii)
    reg_theta = []
end

for i=1:size(theta)

    if i == 1
        grad(i) = grad_temp(i)
    else
        grad(i) = thetas_sum(i)
    end
end
end

And the cost function is giving correct results, but I have no idea why the gradient (one step) is not, the cost gives J = 0.6931 which is correct and the gradient grad = 0.3603 -0.1476 0.0320, which is not, the cost starts from 2 because the parameter theta(1) does not have to be regularized, any help? I guess there is something wrong with the code, but after 4 days I can't see it.Thanks

Answer 1

Finally got it, after rewriting it again like for the 4th time, this is the correct code:

function [J, grad] = costFunctionReg(theta, X, y, lambda)
J = 0;
grad = zeros(size(theta));

temp_theta = [];

for jj = 2:length(theta)

    temp_theta(jj) = theta(jj)^2;
end

theta_reg = lambda/(2*m)*sum(temp_theta);

temp_sum =[];

for ii =1:m

   temp_sum(ii) = -y(ii)*log(sigmoid(theta'*X(ii,:)'))-(1-y(ii))*log(1-sigmoid(theta'*X(ii,:)'));

end

tempo = sum(temp_sum);

J = (1/m)*tempo+theta_reg;

%regulatization
%theta 0

reg_theta0 = 0;

for i=1:m
    reg_theta0(i) = ((sigmoid(theta'*X(i,:)'))-y(i))*X(i,1)
end

theta_temp(1) = (1/m)*sum(reg_theta0)

grad(1) = theta_temp

sum_thetas = []
thetas_sum = []

for j = 2:size(theta)
    for i = 1:m

        sum_thetas(i) = ((sigmoid(theta'*X(i,:)'))-y(i))*X(i,j)
    end

    thetas_sum(j) = (1/m)*sum(sum_thetas)+((lambda/m)*theta(j))
    sum_thetas = []
end

for z=2:size(theta)
    grad(z) = thetas_sum(z)
end


% =============================================================

end

If its helps anyone, or anyone has any comments on how can I do it better. :)