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bmcparams.m
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bmcparams.m
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function covvy=bmcparams(covvy)
% Use MAP for the width parameters of our GP fit - requires checking out
% the logL's in covvy. Also means I'm just going to flat out recompute
% everything below everytime this is called - actually not if there's only
% a single sample
if isfield(covvy, 'derivs_cov')
derivs = covvy.derivs_cov;
else
try
[K DK] = covvy.covfn(covvy.hypersamples(1).hyperparameters, ...
'deriv hyperparams');
derivs=true;
catch
derivs=false;
end
end
if isfield(covvy, 'store_full_kron_prod')
store_full_kron_prod = covvy.store_full_kron_prod;
else
store_full_kron_prod = true;
covvy.store_full_kron_prod = store_full_kron_prod;
end
lowr.UT=true;
lowr.TRANSA=true;
uppr.UT=true;
%allow for possibility of either integer or real hyperparams
num_hps=numel(covvy.hyperparams);
hps=1:num_hps;
if ~isfield(covvy,'widthfrac')
covvy.widthfrac=0.20;
end
widthfrac=covvy.widthfrac;
if derivs
for hyperparam=hps
IndepSamples=covvy.hyperparams(hyperparam).samples;
priorMean=covvy.hyperparams(hyperparam).priorMean;
priorSD=covvy.hyperparams(hyperparam).priorSD;
if ~all(~isnan([IndepSamples;priorMean;priorSD])) ...
|| strcmp(covvy.hyperparams(hyperparam).type,'inactive');
% This hyperparameter is a dummy - ignore it
hps=setdiff(hps,hyperparam);
end
end
KSinv_NS=ones(1,length(hps)+1);
cholKsL=1;
NSamplesPrev=1;
notignored=0;
for hyperparam=hps
type=covvy.hyperparams(hyperparam).type;
IndepSamples=covvy.hyperparams(hyperparam).samples;
NIndepSamples=covvy.hyperparams(hyperparam).NSamples;
priorMean=covvy.hyperparams(hyperparam).priorMean;
priorSD=covvy.hyperparams(hyperparam).priorSD;
NSamples=NSamplesPrev*NIndepSamples;
notignored=notignored+1;
width=widthfrac*separation(IndepSamples);
KsQ=matrify(@(x,y) normpdf(x,y,width),IndepSamples,IndepSamples);
KsQ = improve_covariance_conditioning(KsQ);
cholKsQ=chol(KsQ);
DKs=matrify(@(x,y) (x-y)/width^2.*...
normpdf(x,y,width),IndepSamples,IndepSamples);
% the variable you're taking the derivative wrt is negative
DKsD=matrify(@(x,y) 1/width^2*(1-((x-y)/width).^2).*...
normpdf(x,y,width),IndepSamples,IndepSamples);
KsL=[KsQ,DKs;-DKs,DKsD];
cholKsL=kron2d(cholKsL,updatechol(KsL,cholKsQ,NIndepSamples+1:length(KsL)));
remove=4;
% This is not a parameter - equal to 2^2 due to structure
% of cov matrix
for ind=1:notignored-1
cholKsL=downdatechol(cholKsL,(remove-1)*NSamples+1:remove*NSamples);
remove=remove+1;
end
switch lower(type)
case 'real'
PrecX=(priorSD^2+width^2-priorSD^4/(priorSD^2+width^2))^(-1);
PrecY=(priorSD^2-(priorSD^2+width^2)^2/(priorSD^2))^(-1);
% NSfn2=@(x,y) mvnpdf([x;y],[SamplesMean(d);SamplesMean(d)],...
% [SamplesSD(d)^2+width^2,SamplesSD(d)^2;SamplesSD(d)^2,SamplesSD(d)^2+width^2]);
const = (4*pi^2*(priorSD^2+width^2)/PrecX)^(-0.5);
NSfn=@(x,y) const*...
exp(-0.5*PrecX*((x-priorMean).^2+(y-priorMean).^2)-...
PrecY.*(x-priorMean).*(y-priorMean));
BS=-width^-2*(repmat(IndepSamples',NIndepSamples,1)-priorMean-...
matrify(@(x,y) (PrecX+PrecY)*priorSD^2*...
((x-priorMean)+(y-priorMean)),IndepSamples,IndepSamples));
case 'bounded'
NSfn=@(x,y) normpdf(x,y,sqrt(2)*width).*...
(normcdf(priorMean-priorSD,0.5*(x+y),sqrt(0.5)*width)...
-normcdf(priorMean+priorSD,0.5*(x+y),sqrt(0.5)*width));
case 'mixture'
mixtureWeights = covvy.hyperparams(hyperparam).mixtureWeights;
PrecX=(priorSD.^2+width^2-priorSD.^4./(priorSD.^2+width^2)).^(-1);
PrecY=(priorSD.^2-(priorSD.^2+width^2)^2./(priorSD.^2)).^(-1);
const = (4*pi^2*(priorSD.^2+width^2)./PrecX).^(-0.5);
NSfn = @(x,y) mixture_NSfn(x,y,mixtureWeights,const,...
PrecX,PrecY,priorMean);
end
NS=...%diag(normpdf(IndepSamples,SamplesMean(d),SamplesSD(d)));
matrify(NSfn,IndepSamples,IndepSamples);
% NB: (PrecX+PrecY)*priorSD^2 == priorSD^2/(width^2+2*priorSD^2)
left=(length(hps)+1-notignored)*NSamplesPrev;
% derivs are listed in reverse order
right=(length(hps)+1-notignored+1)*NSamplesPrev;
% NB: first block of KSinv_NS has nothing to do with derivs
KSinv_NS_new=cholKsQ\(cholKsQ'\NS);
KSinv_NS=...
[kron2d(KSinv_NS(:,1:left),KSinv_NS_new),...
kron2d(KSinv_NS(:,left+1:right),cholKsQ\(cholKsQ'\(BS.*NS))),...
kron2d(KSinv_NS(:,right+1:end),KSinv_NS_new)];
NSamplesPrev=NSamples;
end
covvy.KSinv_NS_KSinv=(KSinv_NS/cholKsL)/cholKsL';
elseif ~derivs
if store_full_kron_prod
KSinv_NS_KSinv=1;
cholKS = 1;
else
KSinv_NS_KSinv=cell(num_hps,1);
cholKS = cell(num_hps,1);
end
for hyperparam=hps
type=covvy.hyperparams(hyperparam).type;
if strcmp(type,'discrete')
% For discrete, we assume we have a sample at every position.
priors = covvy.hyperparams(hyperparam).priors;
KSinv_NS_KSinv_hp = diag(priors);
IndepSamples=covvy.hyperparams(hyperparam).samples;
width=widthfrac*separation(IndepSamples);
KsQ_hp=matrify(@(x,y) normpdf(x,y,width),IndepSamples,IndepSamples);
cholKsQ_hp=chol(KsQ_hp);
if store_full_kron_prod
KSinv_NS_KSinv = kron2d(KSinv_NS_KSinv,KSinv_NS_KSinv_hp);
cholKS = kron2d(cholKS,cholKsQ_hp);
else
KSinv_NS_KSinv{hyperparam}=KSinv_NS_KSinv_hp;
cholKS{hyperparam} = cholKsQ_hp;
end
else
IndepSamples=covvy.hyperparams(hyperparam).samples;
NIndepSamples=covvy.hyperparams(hyperparam).NSamples;
priorMean=covvy.hyperparams(hyperparam).priorMean;
priorSD=covvy.hyperparams(hyperparam).priorSD;
if ~all(~isnan([IndepSamples;priorMean;priorSD])) ...
|| strcmp(type,'inactive');
% This hyperparameter is a dummy - ignore it
continue
end
width=widthfrac*separation(IndepSamples);
% fmincon(@(activeTheta) negLogLikelihood(exp(logL),IndepSamples,activeTheta,active,Priorwidth),...
% MLwidth(active),[],[],[],[],zeros(length(active),1),largeLimit,[],optimoptions);
KsQ=matrify(@(x,y) normpdf(x,y,width),IndepSamples,IndepSamples);
% KsQ = improve_covariance_conditioning(KsQ);
cholKsQ=chol(KsQ);
cholKsL=cholKsQ;
% DKs=matrify(@(x,y) (x-y)/width^2.*normpdf(x,y,width),IndepSamples,IndepSamples); % the variable you're taking the derivative wrt is negative
% DKsD=matrify(@(x,y) 1/width^2*(1-((x-y)/width).^2).*normpdf(x,y,width),IndepSamples,IndepSamples);
% KsL=[KsQ,DKs;-DKs,DKsD];
% cholKsL=updatechol(KsL,KsQ,NIndepSamples+1:length(KsL));
switch lower(type)
case 'real'
PrecX=(priorSD^2+width^2-priorSD^4/(priorSD^2+width^2))^(-1);
PrecY=(priorSD^2-(priorSD^2+width^2)^2/(priorSD^2))^(-1);
% NSfn2=@(x,y) mvnpdf([x;y],[SamplesMean(d);SamplesMean(d)],...
% [SamplesSD(d)^2+width^2,SamplesSD(d)^2;SamplesSD(d)^2,SamplesSD(d)^2+width^2]);
const = (4*pi^2*(priorSD^2+width^2)/PrecX)^(-0.5);
NSfn=@(x,y) const*...
exp(-0.5*PrecX*((x-priorMean).^2+(y-priorMean).^2)-...
PrecY.*(x-priorMean).*(y-priorMean));
case 'bounded'
NSfn=@(x,y) normpdf(x,y,sqrt(2)*width).*...
(normcdf(priorMean-priorSD,0.5*(x+y),sqrt(0.5)*width)-normcdf(priorMean+priorSD,0.5*(x+y),sqrt(0.5)*width));
case 'mixture'
mixtureWeights = covvy.hyperparams(hyperparam).mixtureWeights;
PrecX=(priorSD.^2+width^2-priorSD.^4./(priorSD.^2+width^2)).^(-1);
PrecY=(priorSD.^2-(priorSD.^2+width^2)^2./(priorSD.^2)).^(-1);
const = (4*pi^2*(priorSD.^2+width^2)./PrecX).^(-0.5);
NSfn = @(x,y) mixture_NSfn(x,y,mixtureWeights,const,PrecX,PrecY,priorMean);
end
NS=...%diag(normpdf(IndepSamples,SamplesMean(d),SamplesSD(d)));
matrify(NSfn,IndepSamples,IndepSamples);
KSinv_NS_KSinv_hp=cholKsQ\(cholKsQ'\((NS/cholKsL)/cholKsL'));
if store_full_kron_prod
KSinv_NS_KSinv = kron2d(KSinv_NS_KSinv,KSinv_NS_KSinv_hp);
cholKS = kron2d(cholKS,cholKsQ);
else
KSinv_NS_KSinv{hyperparam}=KSinv_NS_KSinv_hp;
cholKS{hyperparam} = cholKsQ;
end
end
end
covvy.KSinv_NS_KSinv=KSinv_NS_KSinv;
covvy.cholKS=cholKS;
end
function s = separation(ls)
if length(ls)<=1
s=1;
else
s=(max(ls)-min(ls))/(length(ls)-1);
end
function NS = mixture_NSfn(x,y,weights,const,PrecX,PrecY,priorMean)
NS = 0;
for i = 1:length(weights)
NS = NS + const(i)*...
exp(-0.5*PrecX(i)*((x-priorMean(i)).^2+(y-priorMean(i)).^2)-...
PrecY(i).*(x-priorMean(i)).*(y-priorMean(i)));
end