The normal equations

ml_normalEquations.m

disp("Use the normal equations without training to get linear regression weights...");

function W = randWeights(in, out)
    epsilon_init = sqrt(6) / sqrt(in + out);
    W = rand(in, out) * 2 * epsilon_init - epsilon_init;
endfunction

% Gen data with m rows and n feature columns.
m = 5000; % m rows data
n = 100; % input features numbers

X = randWeights(m, n);
Y = X * randWeights(n, 1);

% Split 80% of data for traning and the rest for validation.

sp = (m * 0.8);

% Traning data
X_train = X(1:sp, :);
Y_train = Y(1:sp);
% Cross validation data
X_cv = X(m - sp:end, :);
Y_cv = Y(m - sp:end);

function [W] = NE_Training(X, Y)
    W = pinv(X' * X) * X' * Y;
endfunction

W = NE_Training(X_train, Y_train);

% Do hypothsis with W on the cross validation data.

hx = X_cv * W;

function checkHypothsis(Y_cv, hx)
    diff = norm(Y_cv - hx) / norm(Y_cv + hx);

    checkSign = "𐄂";

    if (diff < 1e-9)
        checkSign = "✓";
    endif

    printf(['\nGradients check difference(less than 1e-9).: %g (%s)\n'], diff, checkSign);

endfunction

checkHypothsis(Y_cv, hx);