more rls things

rls/KernelMatrix.m

@@ -0,0 +1,8 @@
+function K = KernelMatrix(X,kernelfun);
+[N,d] = size(X);
+K=zeros(N);
+for i=1:N
+    for j=1:N
+        K(i,j)=kernelfun(X(i,:),X(j,:));
+    end;
+end;

rls/kernel_gauss.m

@@ -0,0 +1,9 @@
+function d = kernel_gauss(a,b);
+sigma = 500000;
+
+N=size(a,1);
+if N==1
+    d=exp(-( (sum((a-b).^2)) ./ (sigma^2) ));
+else
+   d=exp(-(      sum(  ( a-repmat(b,[N 1]))'.^2  )   ./ (sigma^2)     ))';
+end;

rls/kernel_lin.m

@@ -0,0 +1,2 @@
+function d = kernel_lin(a,b);
+d=a*b';

rls/kernel_poly.m

@@ -0,0 +1,3 @@
+function d = kernel_gauss(a,b);
+deg = 5;
+d=(a*b'+1).^deg;

rls/rlsAssignkernelfun.m

@@ -0,0 +1,10 @@
+switch whichKernel
+    case 'linear'
+        kernelfun = @kernel_lin;
+    case 'gaussian'
+        kernelfun = @kernel_gauss;
+    case 'polynomial'
+        kernelfun = @kernel_poly;
+    otherwise
+        error('specified kernel not found');
+end

rls/rlsKernelMatrix.m

@@ -0,0 +1,8 @@
+function K = KernelMatrix(X,kernelfun);
+N= numel(X);
+K=zeros(N);
+for i=1:N
+    for j=1:N
+        K(i,j)=kernelfun(X(j),X(i));
+    end;
+end;

rls/rlsLOO.m

@@ -0,0 +1,37 @@
+function [looe,coeffs] = rlsLOO(Ytrain,Ktrain,lambdas)
+%efficient leave one out error for a set of lambdas
+% function looe = rlsLOO(Ytrain,Ktrain,lambdas)
+%
+% returns:
+% looe vector of loo errors, one per supplied lambda
+% coeffs optimal RLS coefficients for all lambdas
+%
+% takes:
+% Ytrain training labels
+% Ktrain Kernel Matrix of training set
+% lambdas set of resularization parameters
+
+%% eigendecompose Ktrain
+[Q,v]=eig(Ktrain);
+N=size(Ktrain,2);
+
+%% run different lambdas:
+for l=1:length(lambdas)
+
+    % get coeffs
+    Ginv = Q*diag(1./(diag(v)+lambdas(l)))*Q'; 
+    coeffs(:,l)=Ginv*Ytrain;
+
+    % compute leave-one-out error
+    looe(l)= sum( ( coeffs(:,l)./diag(Ginv)  ).^2 );
+
+    %{
+    %sanitycheck
+    KGinv=Ktrain*Ginv;
+    KGinvy=KGinv*Ytrain;
+    for i=1:N
+        y(i) = (KGinvy(i)-KGinv(i,i)*Ytrain(i))./(1-KGinv(i,i));
+    end;
+    looe(l)= sum(      ( Ytrain-y'  ).^2         );
+    %}
+end;