[regression] gradient descent code

regression/code/gradientDescentCubic.m

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+function [c, cs, mses] = gradientDescentCubic(x, y, c0, epsilon, threshold)
+% Gradient descent for fitting a cubic relation.
+%
+% Arguments: x, vector of the x-data values.
+%            y, vector of the corresponding y-data values.
+%            c0, initial value for the parameter c. 
+%            epsilon: factor multiplying the gradient.
+%            threshold: minimum value for gradient
+%
+% Returns:   c, the final value of the c-parameter.
+%            cs: vector with all the c-values traversed.
+%            mses: vector with the corresponding mean squared errors
+  c = c0;
+  gradient = 1000.0;
+  cs = [];
+  mses = [];
+  count = 1;
+  while abs(gradient) > threshold
+      cs(count) = c;
+      mses(count) = meanSquaredErrorCubic(x, y, c);
+      gradient = meanSquaredGradientCubic(x, y, c);
+      c = c - epsilon * gradient; 
+      count = count + 1;
+  end
+end

regression/code/plotgradientdescentcubic.m

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+meansquarederrorline                % generate data
+
+c0 = 2.0;
+eps = 0.0001;
+thresh = 0.1;
+[cest, cs, mses] = gradientDescentCubic(x, y, c0, eps, thresh);
+
+subplot(2, 2, 1);                   % top left panel
+hold on;
+plot(cs, '-o');
+plot([1, length(cs)], [c, c], 'k'); % line indicating true c value
+hold off;
+xlabel('Iteration');
+ylabel('C');
+subplot(2, 2, 3);                   % bottom left panel
+plot(mses, '-o');
+xlabel('Iteration steps');
+ylabel('MSE');
+subplot(1, 2, 2);                   % right panel
+hold on;
+% generate x-values for plottig the fit:
+xx = min(x):0.01:max(x);
+yy = cest * xx.^3;
+plot(xx, yy, 'displayname', 'fit');
+plot(x, y, 'o', 'displayname', 'data'); % plot original data
+xlabel('Size [m]');
+ylabel('Weight [kg]');
+legend("location", "northwest");
+pause