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cigp_sequen.m
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cigp_sequen.m
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function model = cigp_sequen(xTr, yTr, xTe, kernel, ntr, option)
% conditional independet (i.e., coregionalization matrix = I) GP for
% multivariate output with sequencial learning
% WeiXing. May 2020
%
% kernel = 'ard' or 'linear'
%
% logg: v1: initial version. Default normalization
% seque: with sequential learning. Not all xTr/yTr would be used
% sequential setting
if nargin < 6
option.step = 1; %the step of increasing the training data
option.initial_size = 5; %the initial size of training data
end
% optimizer setting
opt = [];
opt.MaxIter = 100;
opt.MaxFunEvals = 10000;
%% default using normalization for x and y
nSample_tr = size(xTr,1);
nSample_te = size(xTe,1);
% dimX =
%for x
%seperate each dim
meanX = mean(xTr);
stdX = std(xTr);
%combine each dim
% meanX = repmat(mean(xTr(:)), 1,size(xTr,2));
% stdX = repmat(std(xTr(:)), 1,size(xTr,2));
%normalize data
xTr = (xTr - repmat(meanX, nSample_tr, 1) ) ./ (repmat(stdX, nSample_tr, 1) + eps);
xTe = (xTe - repmat(meanX, nSample_te, 1) ) ./ (repmat(stdX, nSample_te, 1) + eps);
%for y
%seperate each dim
% meanY = mean(yTr);
% stdY = std(yTr);
%combine each dim
meanY = repmat(mean(yTr(:)), 1,size(yTr,2));
stdY = repmat(std(yTr(:)), 1,size(yTr,2));
%normalize data(
yTr = (yTr - repmat(meanY,nSample_tr,1) ) ./ (repmat(stdY,nSample_tr,1) + eps);
%% add noise for model stability (prevent beta from going to inf)
% yTr = yTr + randn(size(yTr)) ./ 100;
%% init parameters
assert(size(xTr,1)==size(yTr,1),'inconsistent data');
[N,d] = size(xTr);
id_use = 1:option.initial_size;
id_candidate = setdiff(1:nSample_tr,id_use);
% log_bta = log(1/var(yTr(:)));
log_bta = log(1/1e-4);
% log_bta = log(1/eps);
log_l = zeros(d,1);
%log_l = 2*log(median(pdist(Xtr)))*ones(d,1);
log_sigma = 0;
% log_sigma0 = log(1e-4);
log_sigma0 = log(eps);
params = [log_l;log_sigma;log_sigma0;log_bta];
a0 = 1e-3; b0 = 1e-3; %parameter for the noise prior, Gamma
%% main
while length(id_use) < ntr
ixTr = xTr(id_use,:);
iyTr = yTr(id_use,:);
[iN,d] = size(ixTr);
m = size(iyTr,2);
D = iyTr*iyTr';
%fastDerivativeCheck(@(params) log_evidence_CIGP(params,a0,b0,m, xTr, D, kernel), params);
%max_iter = 1000;
%new_param = minimize(param, @(param) log_evidence_lower_bound(param, x, y, m), max_iter);
new_params = minFunc(@(params) log_evidence_CIGP(params,a0,b0,m, ixTr, D, kernel), params, opt);
% params = new_params;
[ker_param,idx] = load_kernel_parameter(new_params, d, kernel, 0);
bta = exp(new_params(idx+1));
%candidate pred
xTr_candiddate = xTr(id_candidate,:);
Sigma = 1/bta*eye(iN) + ker_func(ixTr,ker_param);
Ksn = ker_cross(xTr_candiddate, ixTr, ker_param);
% mean_candidate = Knn*(Sigma\iyTr);
var_candidate = diag(ker_cross(xTr_candiddate,xTr_candiddate,ker_param)) - diag(Ksn*(Sigma\Ksn'));
% yTe_var = var_candidate + 1/bta;
[~, I] = sort(var_candidate,'descend');
import_list = id_candidate(I);
% update id_use
if length(id_use) + option.step > ntr %last update if condition is met
id_use = [id_use, import_list(1: ntr - length(id_use) )];
ixTr = xTr(id_use,:);
iyTr = yTr(id_use,:);
[iN,d] = size(ixTr);
m = size(iyTr,2);
D = iyTr*iyTr';
new_params = minFunc(@(params) log_evidence_CIGP(params,a0,b0,m, ixTr, D, kernel), params, opt);
params = new_params;
else
id_use = [id_use, import_list(1: option.step)];
end
id_candidate = setdiff(1:nSample_tr,id_use);
end
%% save
[ker_param,idx] = load_kernel_parameter(params, d, kernel, 0);
bta = exp(params(idx+1));
model = [];
model.params = params;
model.ker_param = ker_param;
model.bta = bta;
model.id_use = id_use;
%% make predictions for xte/xtr
ixTr = xTr(id_use,:);
iyTr = yTr(id_use,:);
[iN,d] = size(ixTr);
% m = size(iyTr,2);
% D = iyTr*iyTr';
%tr pred
Sigma = 1/bta*eye(iN) + ker_func(ixTr,ker_param);
Knn = ker_cross(xTr, ixTr, ker_param);
yTr_pred = Knn*(Sigma\iyTr);
%de-normalize
yTr_pred = yTr_pred .* repmat(stdY,size(yTr_pred,1),1) + repmat(meanY,size(yTr_pred,1),1);
model.yTr_pred = yTr_pred;
%te pred
if ~isempty(xTe)
Ksn = ker_cross(xTe,ixTr,ker_param);
yTe_pred = Ksn*(Sigma\iyTr);
fTe_var = diag(ker_cross(xTe,xTe,ker_param)) - diag(Ksn*(Sigma\Ksn'));
yTe_var = fTe_var + 1/bta;
%de-normalize
yTe_pred = yTe_pred .* repmat(stdY,size(yTe_pred,1),1) + repmat(meanY,size(yTe_pred,1),1);
model.yTe_pred = yTe_pred;
model.fTe_var = repmat(fTe_var,1,size(yTr,2)) .* repmat(stdY,size(yTe_pred,1),1);
model.yTe_var = repmat(yTe_var,1,size(yTr,2)) .* repmat(stdY,size(yTe_pred,1),1);
end
% xTr = (xTr - repmat(meanX,size(xTr,1)) ) ./ repmat(stdX,size(xTr,1));
% yTr = (yTr - repmat(meanY,size(yTr,1)) ) ./ repmat(stdY,size(yTr,1));
% xTe = (xTe - repmat(meanX,size(xTe,1)) ) ./ repmat(stdX,size(xTe,1));
model.forward = @forward; %prediction function
%save the predictive function
function [yTe_pred,fTe_var]=forward(xTe)
xTe = (xTe - repmat(meanX,size(xTe,1),1) ) ./ (repmat(stdX,size(xTe,1),1) + eps);
Ksn = ker_cross(xTe,ixTr,ker_param);
yTe_pred = Ksn*(Sigma\iyTr);
fTe_var = diag(ker_cross(xTe,xTe,ker_param)) - diag(Ksn*(Sigma\Ksn'));
yTe_var = fTe_var + 1/bta;
%de-normalize
yTe_pred = yTe_pred .* repmat(stdY,size(yTe_pred,1),1) + repmat(meanY,size(yTe_pred,1),1);
% model.yTe_pred = yTe_pred;
fTe_var = repmat(fTe_var,1,size(yTr,2)) .* repmat(stdY,size(yTe_pred,1),1);
% yTe_var = repmat(yTe_var,1,size(yTr,2)) .* repmat(stdY,size(yTe_pred,1),1);
end
end