% this script loads the x/y used to produce figures in lecture 3:
load polyfitdata.mat

ms=[1 3 5 10];

% this is a "fine grid" set to allow us to plot the estimated functions
pts=-4.5:.01:4.5;
% note: it's important to have the same range to prevent normalization
% screwups due to scaling in degexpand.m

% run leave-one-out CV
for m=1:length(ms)
  % fit to the whole training set
  xx=degexpand(x,ms(m));
  wPoly{m}=pinv(xx)*y;

  % empirical loss:
  etr(m)=mean((y-xx*wPoly{m}).^2);

  % plot the model
  figure;
  plot(x,y,'bo','MarkerSize',10);hold on;
  axis([-5 5 -12 6]); % to make figures look exactly like those on the slides
  plot(pts,degexpand(pts,ms(m))*wPoly{m},'r');
  
  % now run leave-one-out CV
  for i=1:size(x,2)
    % exclude i-th example
    xtr=xx(setdiff(1:10,i),:);
    ytr=y(setdiff(1:10,i));

    % fit to the remaining data
    wCV=pinv(xtr)*ytr;
    
    % test on the i-th example
    xts=xx(i,:);
    yts=y(i);
    err(m,i)=(yts-xts*wCV)^2;
  end
  fprintf(2,'%d: empirical %.4f, LOO %.4f\n',ms(m),etr(m),mean(err(m,:)));
end