% ***** GRADIENT DECENT LOGISTIC REGRESSION ***** %

% m:  Number of data samples
% n:  Number of factors or dependent variables
% p:  Index value of a single sample within the set of m samples
% q:  Index value of an individual feature within the 
%     ith sample's feature (or variable) vector
% x:  Feature vector with n+1 features, i.e. x=[x0 x1 x2 x3] & x0=1
% theta:  Parameter vector with at least n+1 parameters, 
%         i.e. theta=[theta0 theta1 theta2 theta3]
% h:  "Hypothesis" or prediction model, i.e. h=theta*transpose(x)
% J:  Cost function dependent on the parameter values in vector theta 

clear all

% DATA POINTS
x=[1 1 1 1 1;
5 1 7 8 2;
8 1 8 8 1];

y=[1 0 1 1 0];


% MODEL PARAMETERS

% Note: The length of the array "theta" needs to
% equal the number of independent variables
% (i.e. length(theta)=n)

% Initialize theta
theta=[-4 1 1]';

% Initialize alpha
alpha=1.4;

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

for count=1:10    
    
    h=1./(1+exp(-theta'*x));
    
    theta(1)=theta(1)-alpha.*(1/m).*sum((h-y)*x(1,:)');
    theta(2)=theta(2)-alpha.*(1/m).*sum((h-y)*x(2,:)');
    theta(3)=theta(3)-alpha.*(1/m).*sum((h-y)*x(3,:)');
    
J=(1/m).*sum(y'*log(1./(1+exp(-theta'*x)))-(1-y)'*log(1-(1./(1+exp(-theta'*x)))));
plot([1:m],J,'r')
hold on
    
end

% J is the Maximum Likelihood Logistic Regression cost function
% J=-(1/m).*sum(y.*log(h)-(1-y).*log(1-h));  % Regularize with lambda*sum(theta)