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MTGP.m
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classdef MTGP < handle
properties
Xtrain;
ytrain;
covfun;
numParams;
numTasks;
params;
useCorrelatedNoise;
rankKf;
rankKn;
end
methods
function obj = MTGP(covfun, numParams, numTasks, useCorrelatedNoise, params, rankKf, rankKn)
obj.covfun = covfun;
obj.numParams = numParams;
obj.numTasks = numTasks;
if nargin>=4
obj.useCorrelatedNoise = useCorrelatedNoise;
else
obj.useCorrelatedNoise = 0;
end
if nargin>=6
obj.rankKf = rankKf;
else
obj.rankKf = numTasks;
end
if nargin>=7
obj.rankKn = rankKn;
else
obj.rankKn = numTasks;
end
if nargin>=5
obj.params = params;
else
if ~obj.useCorrelatedNoise
obj.params = log(10.^(2*(rand(1,obj.numParams+obj.numTasks+1+obj.numTasks*obj.rankKf)-0.5)));
else
obj.params = log(10.^(2*(rand(1,obj.numParams+1+obj.numTasks*obj.rankKn+1+obj.numTasks*obj.rankKf)-0.5)));
end
end
end
function fval = train(obj, Xtrain, ytrain)
obj.Xtrain = Xtrain;
obj.ytrain = ytrain;
opts = optimset('Display','off','MaxIter',10000, 'TolFun', 1e-50, 'TolX', 1e-50, 'MaxFunEvals', 5000);
[obj.params,fval,exitflag] = fminunc(@(x) obj.get_nlml(x), obj.params,opts);
end
function obj = train_multistart(obj, Xtrain, ytrain, numStarts)
listOfParams = {};
listOfNlml = [];
for i=1:numStarts
if ~obj.useCorrelatedNoise
obj.params = log(10.^(2*(rand(1,obj.numParams+obj.numTasks+1+obj.numTasks*obj.rankKf)-0.5)));
else
obj.params = log(10.^(2*(rand(1,obj.numParams+1+obj.numTasks*obj.rankKn+1+obj.numTasks*obj.rankKf)-0.5)));
end
try
nlml = obj.train(Xtrain, ytrain);
catch
i = i - 1;
continue;
end
listOfNlml = [listOfNlml, nlml];
listOfParams = [listOfParams, obj.params];
end
[~, minIdx] = min(listOfNlml);
obj.params = listOfParams{minIdx};
end
function [kparams, Kf, D] = seperate_params(obj, params)
kparams = params(1:obj.numParams);
if ~obj.useCorrelatedNoise
SigmaN = exp(params((obj.numParams+1):(obj.numParams+obj.numTasks)));
D = diag(SigmaN.^2);
nextIdx = obj.numParams+obj.numTasks+1;
else
D = eye(obj.numTasks) * exp(2*params(obj.numParams+1));
nextIdx = obj.numParams+2;
for i = 1:obj.rankKn
v = params(nextIdx:(nextIdx+obj.numTasks-1));
D = D + v'*v;
nextIdx = nextIdx + obj.numTasks;
end
end
Kf = eye(obj.numTasks) * exp(2*params(nextIdx));
nextIdx = nextIdx + 1;
for i = 1:obj.rankKn
v = params(nextIdx:(nextIdx+obj.numTasks-1));
Kf = Kf + v'*v;
nextIdx = nextIdx + obj.numTasks;
end
end
function nlml = get_nlml(obj, paramsVal)
[kparams, Kf, D] = obj.seperate_params(paramsVal);
Kx = obj.covfun(obj.Xtrain, obj.Xtrain, kparams);
I = eye(size(Kx,1));
y = obj.ytrain(:);
valIdx = find(not(isnan(y)));
y = y(valIdx);
n = length(y);
KXX = kron(Kf, Kx);
KN = kron(D,I);
KXX = KXX(valIdx, valIdx);
KN = KN(valIdx, valIdx);
L = chol(KXX+ KN);
alpha = L\(L'\y);
nlml = 0.5*y'*alpha+sum(log(diag(L)))+0.5*n*log(2*pi);
end
function [predMean,predVar] = predict(obj, Xtest)
[kparams, Kf, D] = obj.seperate_params(obj.params);
Kx = obj.covfun(obj.Xtrain, obj.Xtrain, kparams);
I = eye(size(Kx,1));
y = obj.ytrain(:);
valIdx = find(not(isnan(y)));
y = y(valIdx);
n = length(y);
KXX = kron(Kf, Kx);
KN = kron(D,I);
KXX = KXX(valIdx, valIdx);
KN = KN(valIdx, valIdx);
L = chol(KXX+ KN);
alpha = L\(L'\y);
k = obj.covfun(obj.Xtrain, Xtest, kparams);
kx = kron(Kf, k);
kx = kx(valIdx,:);
kxx = obj.covfun(Xtest, Xtest, kparams);
kxx = kron(Kf, kxx);
predMean = kx'*alpha;
v = L\kx;
predVar = kxx - v'*v;
predMean = reshape(predMean, [size(Xtest,1), obj.numTasks]);
predVar = reshape(diag(predVar), [size(Xtest,1), obj.numTasks]);
end
end
end