Contents

olympval.m

From A First Course in Machine Learning, Chapter 1. Simon Rogers, 31/10/11 [simon.rogers@glasgow.ac.uk]

clear all;close all;

Load the Olympic data and extract the training and validation data

load ../data/olympics

x = male100(:,1);
t = male100(:,2);
pos = find(x>1979);

% Rescale x for numerical reasons
x = x - x(1);
x = x./4;


valx = x(pos:end);
valt = t(pos:end);
x(pos:end) = [];
t(pos:end) = [];

Fit the different models and plot the results

orders = [1 4 8]; %We shall fit models of these orders
% Plot the data
figure(1);hold off
plot(x,t,'bo','markersize',5);
hold all
plot(valx,valt,'ro','markersize',5);
plotx = [min(x):0.01:max(valx)]';
for i = 1:length(orders)
    X = [];
    plotX = [];
    valX = [];
    for k = 0:orders(i)
        X = [X x.^k];
        valX = [valX valx.^k];
        plotX = [plotX plotx.^k];
    end

    % Compute w
    w = inv(X'*X)*X'*t;
    plot(plotx,plotX*w,'linewidth',2);

    % Compute validation loss
    val_loss(i) = mean((valX*w - valt).^2);
end
ylim([9 12]);
legend('Training','Validation','Linear','4th order','8th order');

Warning: Matrix is close to singular or badly scaled.
         Results may be inaccurate. RCOND = 4.009504e-23. 

Display the validation losses

for i = 1:length(orders)
 fprintf('\n Model order: %g, Validation loss: %g',...
        orders(i),val_loss(i));
end

 Model order: 1, Validation loss: 0.101298
 Model order: 4, Validation loss: 4.45706
 Model order: 8, Validation loss: 6023.25

Published with MATLAB® 7.12