(1)    %  rdgpredEfficient prediction using ridge regression.
(2)   %rdgpred(Y,A,A21,L) returns ridge regression predictions in test set.
(3)   %Vector Y contains outcome training set, matrix A similarity measures
(4)   %in training set (e.g., A=XX  for N-by-P input matrix X), matrix A21
(5)   %similarity individuals in test set (rows) and training set (columns),
(6)   %and vector L the penalty values to consider.
(7)   %
(8)   %rdgpred(Y,A,A21,L,Z,Z2) first corrects A and A21 for confounders.
(9)   %Matrix Z contains confounders in traing set and Z2 those in test set.
(10) %
(11)  %Author  : R de Vlaming and PJF Groenen
(12) %Institute: Erasmus School of EconomicsDate: November 25, 2014
(13) function Y2 = rdgpred(Y,A,A21,L,Z,Z2)
(14)
(15) P  = numel(L);  % find size of set of penalties
(16) N  = numel(Y);  % find size of training set
(17) N2 = size(A21,1); % find size of test set
(18)
(19) if nargin > 5    % correct similarities if confounders present
(20)  M  = eye(N) Zinv(ZZ)Z;% anti projection matrix of Z
(21)   M2  = eye(N2)  -  Z2inv(Z2Z2)Z2;  % anti projection matrix of Z2
(22)  A  = MAM;% adjust similarties A
(23)  A21 = M2A21M;% adjust similarties A21
(24) end
(25)
(26) [Q,D] = eig(A); D = diag(D); % obtain eigenvecs Q and eigenvalues D of A
(27)
(28) % for each eigenvalue E (rows) and lambda S (cols) find 1/(E+S)
(29) D = 1./(repmat(D,1,P) + repmat(L(:),N,1));
(30)
(31) % predict for observations in test set (rows) for each lambda (cols)
(32) QTY = repmat((YQ),1,P);
(33) Y2  = A21(Q(D.QTY));
(34) Y2  = real(Y2); % remove imaginary part due to numerical imprecession
(35)
(36) end
Algorithm 1: MATLAB code for efficient ridge regression prediction: rdgpred.m.