1 function U04_test_CV_krr
   2 
   3 % Generate data.
   4 n = 20;
   5 x = linspace(-1, 1, n);
   6 y = [ 1.153741e+00, 8.145612e-01, 4.369920e-01, 4.227247e-01, 2.699726e-01, 2.347085e-01, 1.136709e-01, 4.134774e-02, -4.843545e-02, -3.683275e-03, -1.416303e-01, 8.616478e-02, -6.309822e-02, 6.957640e-02, 2.097653e-01, 3.599886e-01, 4.604808e-01, 7.970857e-01, 9.627512e-01, 1.062644e+00 ];
   7 
   8 % Plot data. 
   9 clf; hold on;
  10 plot(x,y,'bo');
  11 
  12 % Select kernel width sigma using 10x10-CV using squared loss. 
  13 [M,opt_param] = cv(x,y,@(tr_x,tr_y,sigma) krr(tr_x,tr_y,'gaussian',sigma), ...
  14         { 'sigma', logspace(0,1,10) }, [], [], @loss_squared);
  15 
  16 % Compute and plot predictions.
  17 xx = linspace(-1,1,200);
  18 yy = apply(M,xx);
  19 plot(xx,yy,'r--');
  20 
  21 % Plot truth. 
  22 plot(xx,f(xx),'b--');
  23 
  24 legend('Data', 'Predictions', 'Truth');
  25 title(sprintf('Kernel width selected by CV: %f', opt_param.sigma));
  26 
  27 % Squared loss.
  28 function sqloss = loss_squared(X,y_true,y_pred)
  29 sqloss = y_true-y_pred;
  30 sqloss = sum(sqloss(:).^2);
  31 
  32 % True regression function.
  33 function y = f(x) 
  34 y = x.^2;
  35 
  36 % Apply function.
  37 function y = apply(M,X)
  38 y = feval(M.applyfunc, M, X);