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sample_theta.m
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sample_theta.m
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function theta = sample_theta(theta,Ustats,obsModel,Kextra)
prior_params = obsModel.params;
switch obsModel.type
case 'Multinomial'
p = theta.p;
store_counts = Ustats.card;
alpha_vec = prior_params.alpha;
[Kz Ks] = size(store_counts);
for kz=1:Kz
for ks = 1:Ks
p(kz,ks,:) = randdirichlet([alpha_vec'+store_counts(:,kz,ks)])';
end
end
theta.p = p;
case {'Gaussian','AR','SLDS'}
theta = sample_theta_submodule(theta,Ustats,obsModel.priorType,prior_params,Kextra);
if strcmp(obsModel.type,'SLDS')
y_prior_params = obsModel.y_params;
theta.theta_r = sample_theta_submodule(theta.theta_r,Ustats.Ustats_r,obsModel.y_priorType,y_prior_params,[]);
end
end
return;
function theta = sample_theta_submodule(theta,Ustats,priorType,prior_params,Kextra)
nu = prior_params.nu;
nu_delta = prior_params.nu_delta;
store_card = Ustats.card;
if size(store_card,1)==1
store_card = store_card';
end
store_card = [store_card; zeros(Kextra,size(store_card,2))];
[Kz Ks] = size(store_card);
switch priorType
case 'MNIW'
invSigma = theta.invSigma;
A = theta.A;
store_XX = Ustats.XX;
store_YX = Ustats.YX;
store_YY = Ustats.YY;
store_sumY = Ustats.sumY;
store_sumX = Ustats.sumX;
K = prior_params.K;
M = prior_params.M;
MK = prior_params.M*prior_params.K;
MKM = MK*prior_params.M';
for kz=1:Kz
for ks=1:Ks
if store_card(kz,ks)>0
%% Given X, Y get sufficient statistics
Sxx = store_XX(:,:,kz,ks) + K;
Syx = store_YX(:,:,kz,ks) + MK;
Syy = store_YY(:,:,kz,ks) + MKM;
SyxSxxInv = Syx/Sxx;
Sygx = Syy - SyxSxxInv*Syx';
Sygx = (Sygx + Sygx')/2;
else
Sxx = K;
SyxSxxInv = M;
Sygx = 0;
end
% Sample Sigma given s.stats
[sqrtSigma sqrtinvSigma] = randiwishart(Sygx + nu_delta,nu+store_card(kz,ks));
invSigma(:,:,kz,ks) = sqrtinvSigma'*sqrtinvSigma;
% Sample A given Sigma and s.stats
cholinvSxx = chol(inv(Sxx));
A(:,:,kz,ks) = sampleFromMatrixNormal(SyxSxxInv,sqrtSigma,cholinvSxx);
end
end
theta.invSigma = invSigma;
theta.A = A;
case 'NIW'
invSigma = theta.invSigma;
mu = theta.mu;
store_YY = Ustats.YY;
store_sumY = Ustats.sumY;
K = prior_params.K;
M = prior_params.M;
MK = prior_params.M*prior_params.K;
MKM = MK*prior_params.M';
for kz=1:Kz
for ks=1:Ks
if store_card(kz,ks)>0
%% Given X, Y get sufficient statistics
Sxx = store_card(kz,ks) + K;
Syx = store_sumY(:,kz,ks) + MK;
Syy = store_YY(:,:,kz,ks) + MKM;
SyxSxxInv = Syx/Sxx;
Sygx = Syy - SyxSxxInv*Syx';
Sygx = (Sygx + Sygx')/2;
else
Sxx = K;
SyxSxxInv = M;
Sygx = 0;
end
% Sample Sigma given s.stats
[sqrtSigma sqrtinvSigma] = randiwishart(Sygx + nu_delta,nu+store_card(kz,ks));
invSigma(:,:,kz,ks) = sqrtinvSigma'*sqrtinvSigma;
% Sample A given Sigma and s.stats
cholinvSxx = chol(inv(Sxx));
mu(:,kz,ks) = sampleFromMatrixNormal(SyxSxxInv,sqrtSigma,cholinvSxx);
end
end
theta.invSigma = invSigma;
theta.mu = mu;
case {'MNIW-N'}
invSigma = theta.invSigma;
A = theta.A;
mu = theta.mu;
store_XX = Ustats.XX;
store_YX = Ustats.YX;
store_YY = Ustats.YY;
store_sumY = Ustats.sumY;
store_sumX = Ustats.sumX;
% If MNIW-N, K and M are as in MNIW. If IW-N, K=1 and M=0.
K = prior_params.K;
M = prior_params.M;
MK = prior_params.M*prior_params.K;
MKM = MK*prior_params.M';
if ~isfield(prior_params,'numIter'), prior_params.numIter = 50; end
numIter = prior_params.numIter;
mu0 = prior_params.mu0;
cholSigma0 = prior_params.cholSigma0;
Lambda0 = inv(prior_params.cholSigma0'*prior_params.cholSigma0);
theta0 = Lambda0*prior_params.mu0;
dimu = size(nu_delta,1);
for kz=1:Kz
for ks=1:Ks
if store_card(kz,ks)>0 %**
for n=1:numIter
%% Given X, Y get sufficient statistics
Sxx = store_XX(:,:,kz,ks) + K;
Syx = store_YX(:,:,kz,ks) + MK - mu(:,kz,ks)*store_sumX(:,kz,ks)';
Syy = store_YY(:,:,kz,ks) + MKM ...
- mu(:,kz,ks)*store_sumY(:,kz,ks)' - store_sumY(:,kz,ks)*mu(:,kz,ks)' + store_card(kz,ks)*mu(:,kz,ks)*mu(:,kz,ks)';
SyxSxxInv = Syx/Sxx;
Sygx = Syy - SyxSxxInv*Syx';
Sygx = (Sygx + Sygx')/2;
% Sample Sigma given s.stats
[sqrtSigma sqrtinvSigma] = randiwishart(Sygx + nu_delta,nu+store_card(kz,ks));
invSigma(:,:,kz,ks) = sqrtinvSigma'*sqrtinvSigma;
% Sample A given Sigma and s.stats
cholinvSxx = chol(inv(Sxx));
A(:,:,kz,ks) = sampleFromMatrixNormal(SyxSxxInv,sqrtSigma,cholinvSxx);
% Sample mu given A and Sigma
Sigma_n = inv(Lambda0 + store_card(kz,ks)*invSigma(:,:,kz,ks));
mu_n = Sigma_n*(theta0 + invSigma(:,:,kz,ks)*(store_sumY(:,kz,ks)-A(:,:,kz,ks)*store_sumX(:,kz,ks)));
mu(:,kz,ks) = mu_n + chol(Sigma_n)'*randn(dimu,1);
end
else
Sxx = K;
SyxSxxInv = M;
Sygx = 0;
[sqrtSigma sqrtinvSigma] = randiwishart(nu_delta,nu);
invSigma(:,:,kz,ks) = sqrtinvSigma'*sqrtinvSigma;
cholinvK = chol(inv(K));
A(:,:,kz,ks) = sampleFromMatrixNormal(M,sqrtSigma,cholinvK);
mu(:,kz,ks) = mu0 + cholSigma0'*randn(dimu,1);
end
end
end
theta.invSigma = invSigma;
theta.A = A;
theta.mu = mu;
case {'IW-N'}
invSigma = theta.invSigma;
mu = theta.mu;
store_YY = Ustats.YY;
store_sumY = Ustats.sumY;
if ~isfield(prior_params,'numIter'), prior_params.numIter = 50; end
numIter = prior_params.numIter;
mu0 = prior_params.mu0;
cholSigma0 = prior_params.cholSigma0;
Lambda0 = inv(prior_params.cholSigma0'*prior_params.cholSigma0);
theta0 = Lambda0*prior_params.mu0;
dimu = size(nu_delta,1);
for kz=1:Kz
for ks=1:Ks
if store_card(kz,ks)>0 %**
for n=1:numIter
%% Given X, Y get sufficient statistics
Syy = store_YY(:,:,kz,ks) ...
- mu(:,kz,ks)*store_sumY(:,kz,ks)' - store_sumY(:,kz,ks)*mu(:,kz,ks)' + store_card(kz,ks)*mu(:,kz,ks)*mu(:,kz,ks)';
Sygx = (Syy + Syy')/2;
% Sample Sigma given s.stats
[sqrtSigma sqrtinvSigma] = randiwishart(Sygx + nu_delta,nu+store_card(kz,ks));
invSigma(:,:,kz,ks) = sqrtinvSigma'*sqrtinvSigma;
% Sample mu given A and Sigma
Sigma_n = inv(Lambda0 + store_card(kz,ks)*invSigma(:,:,kz,ks));
mu_n = Sigma_n*(theta0 + invSigma(:,:,kz,ks)*store_sumY(:,kz,ks));
mu(:,kz,ks) = mu_n + chol(Sigma_n)'*randn(dimu,1);
end
else
[sqrtSigma sqrtinvSigma] = randiwishart(nu_delta,nu);
invSigma(:,:,kz,ks) = sqrtinvSigma'*sqrtinvSigma;
mu(:,kz,ks) = mu0 + cholSigma0'*randn(dimu,1);
end
end
end
theta.invSigma = invSigma;
theta.mu = mu;
case {'IW-N-tiedwithin'}
invSigma = theta.invSigma;
mu = theta.mu;
store_YY = Ustats.YY;
store_sumY = Ustats.sumY;
if ~isfield(prior_params,'numIter'), prior_params.numIter = 50; end
numIter = prior_params.numIter;
mu0 = prior_params.mu0;
cholSigma0 = prior_params.cholSigma0;
Lambda0 = inv(prior_params.cholSigma0'*prior_params.cholSigma0);
theta0 = Lambda0*prior_params.mu0;
dimu = size(nu_delta,1);
for kz=1:Kz
store_invSigma = invSigma(:,:,kz,1);
for n=1:numIter
% muY = zeros(dimu,dimu);
% muN = zeros(dimu,dimu);
for ks=1:Ks
if store_card(kz,ks)>0
% Sample mu given A and Sigma
Sigma_n = inv(Lambda0 + store_card(kz,ks)*store_invSigma);
mu_n = Sigma_n*(theta0 + store_invSigma*store_sumY(:,kz,ks));
mu(:,kz,ks) = mu_n + chol(Sigma_n)'*randn(dimu,1);
% muY = muY + mu(:,kz,ks)*store_sumY(:,kz,ks)';
% muN = muN + store_card(kz,ks)*mu(:,kz,ks)*mu(:,kz,ks)';
else
mu(:,kz,ks) = mu0 + cholSigma0'*randn(dimu,1);
end
end
%% Given Y get sufficient statistics %**
store_card_kz = store_card(kz,:);
squeeze_mu_kz = squeeze(mu(:,kz,:));
muY = squeeze_mu_kz*squeeze(store_sumY(:,kz,:))';
muN = (repmat(store_card_kz,[dimu 1]).*squeeze_mu_kz)*squeeze_mu_kz';
Syy = sum(store_YY(:,:,kz,:),4) - muY - muY' + muN;
Syy = (Syy + Syy')/2;
% Sample Sigma given s.stats
[sqrtSigma sqrtinvSigma] = randiwishart(Syy + nu_delta,nu+sum(store_card_kz));
store_invSigma = sqrtinvSigma'*sqrtinvSigma;
end
invSigma(:,:,kz,1:Ks) = repmat(store_invSigma,[1 1 1 Ks]);
end
theta.invSigma = invSigma;
theta.mu = mu;
case {'N-IW-N','Afixed-IW-N','ARD'}
invSigma = theta.invSigma;
A = theta.A;
mu = theta.mu;
store_XX = Ustats.XX;
store_YX = Ustats.YX;
store_YY = Ustats.YY;
store_sumY = Ustats.sumY;
store_sumX = Ustats.sumX;
if ~isfield(prior_params,'numIter'), prior_params.numIter = 50; end
numIter = prior_params.numIter;
if ~isfield(prior_params,'zeroMean')
mu0 = prior_params.mu0;
cholSigma0 = prior_params.cholSigma0;
Lambda0 = inv(prior_params.cholSigma0'*prior_params.cholSigma0);
theta0 = Lambda0*prior_params.mu0;
end
r = size(A,2)/size(A,1);
if strcmp(priorType,'N-IW-N')
M = prior_params.M;
Lambda0_A = prior_params.Lambda0_A;
theta0_A = Lambda0_A*M(:);
dim_vecA = numel(M);
XinvSigmaX = zeros(dim_vecA,dim_vecA);
XinvSigmay = zeros(dim_vecA,1);
elseif strcmp(priorType,'ARD')
M = zeros(size(A(:,:,1,1)));
theta0_A = zeros(numel(M),1);
[numRow numCol] = size(M);
dim_vecA = numRow*numCol;
a_ARD = prior_params.a_ARD;
b_ARD = prior_params.b_ARD;
if r == 1
% One hyperparameter per column of SLDS matrix:
numHypers = numCol;
else
% One hyperparameter per lag matrix in VAR matrix:
numHypers = r;
end
%numHypers = numCol;
ARDhypers = ones(numHypers,Kz,Ks);
posInds = find(store_card>0);
if ~isempty(posInds)
ARDhypers(:,1:size(mu,2)) = theta.ARDhypers;
end
end
dimu = size(nu_delta,1);
for n=1:numIter
for kz=1:Kz
for ks=1:Ks
if store_card(kz,ks)>0 %**
% Sample Sigma given A, mu, and s.stats
S = store_YY(:,:,kz,ks) + A(:,:,kz,ks)*store_XX(:,:,kz,ks)*A(:,:,kz,ks)'...
-A(:,:,kz,ks)*store_YX(:,:,kz,ks)' - store_YX(:,:,kz,ks)*A(:,:,kz,ks)'...
- mu(:,kz,ks)*(store_sumY(:,kz,ks)-A(:,:,kz,ks)*store_sumX(:,kz,ks))'- (store_sumY(:,kz,ks)-A(:,:,kz,ks)*store_sumX(:,kz,ks))*mu(:,kz,ks)'...
+ store_card(kz,ks)*mu(:,kz,ks)*mu(:,kz,ks)';
S = 0.5*(S+S');
[sqrtSigma sqrtinvSigma] = randiwishart(S + nu_delta,nu+store_card(kz,ks));
invSigma(:,:,kz,ks) = sqrtinvSigma'*sqrtinvSigma;
if isfield(prior_params,'zeroMean')
mu(:,kz,ks) = zeros(dimu,1);
else
% Sample mu given A, Sigma, and s.stats
% %**
Sigma_n = inv(Lambda0 + store_card(kz,ks)*invSigma(:,:,kz,ks));
mu_n = Sigma_n*(theta0 + invSigma(:,:,kz,ks)*(store_sumY(:,kz,ks)-A(:,:,kz,ks)*store_sumX(:,kz,ks)));
mu(:,kz,ks) = mu_n + chol(Sigma_n)'*randn(dimu,1);
end
if strcmp(priorType,'N-IW-N') %**
XinvSigmaX = XinvSigmaX + kron(store_XX(:,:,kz,ks),invSigma(:,:,kz,ks)); % since A is shared, grow for all data, not just kz,ks
temp = invSigma(:,:,kz,ks)*(store_YX(:,:,kz,ks)-mu(:,kz,ks)*store_sumX(:,kz,ks)');
XinvSigmay = XinvSigmay + temp(:); % since A is shared, grow for all data, not just kz,ks
elseif strcmp(priorType,'ARD') %**
XinvSigmaX = kron(store_XX(:,:,kz,ks),invSigma(:,:,kz,ks));
XinvSigmay = invSigma(:,:,kz,ks)*(store_YX(:,:,kz,ks)-mu(:,kz,ks)*store_sumX(:,kz,ks)');
XinvSigmay = XinvSigmay(:);
ARDhypers_kzks = ARDhypers(:,kz,ks);
if r == 1
numObsPerHyper = numRow;
else
numObsPerHyper = numRow*(numCol/r);
end
ARDhypers_kzks = ARDhypers_kzks(:,ones(1,numObsPerHyper))';
ARDhypers_kzks = ARDhypers_kzks(:);
Lambda0_A = diag(ARDhypers_kzks);
Sigma_A = inv(Lambda0_A + XinvSigmaX);
mu_A = Sigma_A*(theta0_A + XinvSigmay);
vecA = mu_A + chol(Sigma_A)'*randn(dim_vecA,1);
A(:,:,kz,ks) = reshape(vecA,size(M));
AA = sum(A(:,:,kz,ks).*A(:,:,kz,ks),1);
if r>1
AA = reshape(AA,[numCol/r r]);
AA = sum(AA,1);
end
aa = zeros(1,numHypers);
for ii=1:numHypers;
aa(ii) = randgamma(a_ARD + numObsPerHyper/2);
%aa(ii) = randgamma(a_ARD + numRow/2);
end
ARDhypers(:,kz,ks) = aa ./ (b_ARD + AA/2);
end
else
[sqrtSigma sqrtinvSigma] = randiwishart(nu_delta,nu);
invSigma(:,:,kz,ks) = sqrtinvSigma'*sqrtinvSigma;
if isfield(prior_params,'zeroMean')
mu(:,kz,ks) = zeros(dimu,1);
else
mu(:,kz,ks) = mu0 + cholSigma0'*randn(dimu,1);
end
if strcmp(priorType,'ARD')
ARDhypers_kzks = ARDhypers(:,kz,ks);
if r == 1
numObsPerHyper = numRow;
else
numObsPerHyper = numRow*(numCol/r);
end
ARDhypers_kzks = ARDhypers_kzks(:,ones(1,numObsPerHyper))';
ARDhypers_kzks = ARDhypers_kzks(:);
cholSigma_A = diag(1./sqrt(ARDhypers_kzks));
vecA = cholSigma_A'*randn(dim_vecA,1);
A(:,:,kz,ks) = reshape(vecA,size(M));
AA = sum(A(:,:,kz,ks).*A(:,:,kz,ks),1);
if r>1
AA = reshape(AA,[numCol/r r]);
AA = sum(AA,1);
end
aa = zeros(1,numHypers);
for ii=1:numHypers;
aa(ii) = randgamma(a_ARD + numObsPerHyper/2);
%aa(ii) = randgamma(a_ARD + numRow/2);
end
ARDhypers(:,kz,ks) = aa ./ (b_ARD + AA/2);
end
end
end
end
% Possible code speedup: if using fixed A matrix one could put the
% n=1:numIter inside the Kz,Ks loop and precompute
% A*store_XX*A', etc.
if strcmp(priorType,'N-IW-N')
% Code currently assumes shared A if N-IW-N is called,
% but is written below so as to allow easy change to
% Gaussian prior on individual A(:,:,kz,ks) as well
Sigma_A = inv(Lambda0_A + XinvSigmaX);
mu_A = Sigma_A*(theta0_A + XinvSigmay);
vecA = mu_A + chol(Sigma_A)'*randn(dim_vecA,1);
A = repmat(reshape(vecA,size(M)),[1 1 Kz Ks]);
% Reset stored stats:
XinvSigmaX = zeros(dim_vecA,dim_vecA);
XinvSigmay = zeros(dim_vecA,1);
end
end
theta.invSigma = invSigma;
theta.A = A;
theta.mu = mu;
if strcmp(priorType,'ARD')
theta.ARDhypers = ARDhypers;
end
case 'IW'
invSigma = theta.invSigma;
store_YY = Ustats.YY;
store_sumY = Ustats.sumY;
dimu = size(nu_delta,1);
for kz=1:Kz
for ks=1:Ks
if store_card(kz,ks)>0 %**
%% Given X, Y get sufficient statistics
Syy = store_YY(:,:,kz,ks);
Sygx = (Syy + Syy')/2;
% Sample Sigma given s.stats
[sqrtSigma sqrtinvSigma] = randiwishart(Sygx + nu_delta,nu+store_card(kz,ks));
invSigma(:,:,kz,ks) = sqrtinvSigma'*sqrtinvSigma;
else
[sqrtSigma sqrtinvSigma] = randiwishart(nu_delta,nu);
invSigma(:,:,kz,ks) = sqrtinvSigma'*sqrtinvSigma;
end
end
end
theta.invSigma = invSigma;
end
return;