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gpUpdateAD.m
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gpUpdateAD.m
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function model = gpUpdateAD(model, X)
% GPUPDATEAD Update the representations of A and D associated with the model.
% FORMAT
% DESC updates the representations of A and D in the model when
% called by gpUpdateKernels.
% ARG model : the model for which the representations are being
% updated.
% ARG X : the X values for which the representations are being
% computed.
% RETURN model : the model with the A and D representations
% updated.
%
% SEEALSO : gpUpdateKernels, gpExpandParam
%
% COPYRIGHT : Neil D. Lawrence 2006, 2009
% GP
if nargin < 2
X = model.X;
end
qr_decomposition = true;
switch model.approx
case 'ftc'
% Compute the inner product values.
if ~isfield(model, 'S')
if ~isfield(model, 'isSpherical') | model.isSpherical
for i = 1:model.d
model.innerProducts(1, i) = model.m(:, i)'*model.invK_uu...
*model.m(:, i);
end
else
for i = 1:model.d
ind = gpDataIndices(model, i);
model.innerProducts(1, i) = model.m(ind, i)'*model.invK_uu{i}...
*model.m(ind, i);
end
end
end
case {'dtc', 'dtcvar'}
if ~isfield(model, 'isSpherical') | model.isSpherical
% Compute A = invBetaK_uu + K_uf*K_uf'
if ~qr_decomposition
% This can become unstable when K_uf2 is low rank.
K_uf2 = model.K_uf*model.K_uf';
model.A = (1/model.beta)*model.K_uu+ K_uf2;
[model.Ainv, U] = pdinv(model.A);
model.logdetA = logdet(model.A, U);
else
Ruu = jitChol(model.K_uu);
sqrtBeta = sqrt(model.beta);
[Q, R] = qr([Ruu; sqrt(model.beta)*model.K_uf'], '0');
RA = 1/sqrtBeta*R;
model.A = RA'*RA;
model.Ainv = pdinv(model.A, RA);
model.logdetA = logdet(model.A, RA);
end
% compute inner products
for i = 1:model.d
if ~qr_decomposition
E = model.K_uf*model.m(:, i);
model.innerProducts(1, i) = ...
model.beta*(model.m(:, i)'*model.m(:, i) ...
- E'*model.Ainv*E);
else
Z = Q(size(model.K_uu, 1)+1:end, :)'*model.m(:, i);
model.innerProducts(1, i) = ...
model.beta*(model.m(:, i)'*model.m(:, i) ...
- Z'*Z);
end
end
if strcmp(model.approx, 'dtcvar')
model.diagD = model.beta*(model.diagK ...
- sum(model.K_uf.*(model.invK_uu*model.K_uf), 1)');
end
else
if ~model.isMissingData
K_uf2 = model.K_uf*model.K_uf';
end
for i = 1:model.d
ind = gpDataIndices(model, i);
% Compute A = invBetaK_uu + K_uf*K_uf'
if model.isMissingData
K_uf2 = model.K_uf(:, ind)*model.K_uf(:, ind)';
end
model.A{i} = (1/model.beta)*model.K_uu+ K_uf2;
% This can become unstable when K_uf2 is low rank.
[model.Ainv{i}, U] = pdinv(model.A{i});
model.logdetA(i) = logdet(model.A{i}, U);
% compute inner products
E = model.K_uf(:, ind)*model.m(ind, i);
model.innerProducts(1, i) = ...
model.beta*(model.m(ind, i)'*model.m(ind, i) ...
- E'*model.Ainv{i}*E);
end
if strcmp(model.approx, 'dtcvar')
error('Non spherical implementation for dtcvar not yet done.')
end
end
case 'fitc'
model.L = jitChol(model.K_uu)';
if ~isfield(model, 'isSpherical') | model.isSpherical
model.diagD = 1 + model.beta*model.diagK ...
- model.beta*sum(model.K_uf.*(model.invK_uu*model.K_uf), 1)';
% model.diagDdivBeta = 1/model.beta + model.diagK - sum(model.K_uf.*(model.invK_uu*model.K_uf), 1)';
model.Dinv = sparseDiag(1./model.diagD);
% model.betaDinv = sparseDiag(1./model.diagDdivBeta);
K_ufDinvK_uf = model.K_uf*model.Dinv*model.K_uf';
model.A = 1/model.beta*model.K_uu + K_ufDinvK_uf;
% model.betaA = model.K_uu
% This can become unstable when K_ufDinvK_uf is low rank.
[model.Ainv, U] = pdinv(model.A);
model.logDetA = logdet(model.A, U);
% model.detDiff = model.logDetA - model.logDetK_uu;
model.detDiff = - log(model.beta)*model.k + log(det(eye(model.k) + model.beta*K_ufDinvK_uf*model.invK_uu));
% compute inner products
for i = 1:model.d
Dinvm = model.Dinv*model.m(:, i);
K_ufDinvm = model.K_uf*Dinvm;
model.innerProducts(1, i) = model.beta*(Dinvm'*model.m(:, i) ...
- K_ufDinvm'*model.Ainv*K_ufDinvm);
end
% Computations from Ed's implementation.
model.V = model.L\model.K_uf;
model.V = model.V./repmat(sqrt(model.diagD)', model.k, 1);
model.Am = 1/model.beta*eye(model.k)+model.V*model.V';
model.Lm = jitChol(model.Am)';
model.invLmV = model.Lm\model.V;
model.scaledM = model.m./repmat(sqrt(model.diagD), 1, model.d);
model.bet = model.invLmV*model.scaledM;
else
for i = 1:model.d
ind = gpDataIndices(model, i);
model.diagD{i} = 1 + model.beta*model.diagK(ind) ...
- model.beta*sum(model.K_uf(:, ind).*(model.invK_uu*model.K_uf(:, ind)), 1)';
model.Dinv{i} = sparseDiag(1./model.diagD{i});
K_ufDinvK_uf = model.K_uf(:, ind)*model.Dinv{i}...
*model.K_uf(:, ind)';
model.A{i} = 1/model.beta*model.K_uu + K_ufDinvK_uf;
% This can become unstable when K_ufDinvK_uf is low rank.
[model.Ainv{i}, U] = pdinv(model.A{i});
model.logDetA(i) = logdet(model.A{i}, U);
% model.detDiff = model.logDetA - model.logDetK_uu;
model.detDiff(i) = - log(model.beta)*model.k + log(det(eye(model.k) + model.beta*K_ufDinvK_uf*model.invK_uu));
% compute inner products
Dinvm = model.Dinv{i}*model.m(ind, i);
K_ufDinvm = model.K_uf(:, ind)*Dinvm;
model.innerProducts(1, i) = model.beta*(Dinvm'*model.m(ind, i) - K_ufDinvm'*model.Ainv{i}*K_ufDinvm);
% Computations from Ed's implementation.
model.V{i} = model.L\model.K_uf(:, ind);
model.V{i} = model.V{i}./repmat(sqrt(model.diagD{i})', model.k, 1);
model.Am{i} = 1/model.beta*eye(model.k)+model.V{i}*model.V{i}';
model.Lm{i} = jitChol(model.Am{i})';
model.invLmV{i} = model.Lm{i}\model.V{i};
model.scaledM{i} = model.m(ind, i)./sqrt(model.diagD{i});
model.bet{i} = model.invLmV{i}*model.scaledM{i};
end
end
case 'pitc'
if ~isfield(model, 'isSpherical') | model.isSpherical
model.A = 1/model.beta*model.K_uu;
K_ufDinvm = zeros(model.k, model.d);
for i = 1:length(model.blockEnd)
ind = gpBlockIndices(model, i);
model.D{i} = eye(length(ind)) + model.beta*model.K{i} - ...
model.beta*model.K_uf(:, ind)'*model.invK_uu*model.K_uf(:, ind);
[model.Dinv{i}, U] = pdinv(model.D{i});
model.logDetD(i) = logdet(model.D{i}, U);
K_ufDinvK_uf = model.K_uf(:, ind)*model.Dinv{i}...
*model.K_uf(:, ind)';
model.A = model.A + K_ufDinvK_uf;
Dinvm{i} = model.Dinv{i}*model.m(ind, :);
K_ufDinvm = K_ufDinvm + model.K_uf(:, ind)*Dinvm{i};
end
% This can become unstable when K_ufDinvK_uf is low rank.
[model.Ainv, U] = pdinv(model.A);
model.logDetA = logdet(model.A, U);
% compute inner products
for i = 1:model.d
model.innerProducts(1, i) = - model.beta*K_ufDinvm(:, i)'*model.Ainv*K_ufDinvm(:, ...
i);
end
for i = 1:length(model.blockEnd)
ind = gpBlockIndices(model, i);
for j = 1:model.d
model.innerProducts(1, j) = model.innerProducts(1, j) ...
+ model.beta*Dinvm{i}(:, j)'*model.m(ind, j);
end
end
else
for j = 1:model.d
model.A{j} = 1/model.beta*model.K_uu;
K_ufDinvm = zeros(model.k, model.d);
for i = 1:length(model.blockEnd)
ind = gpDataIndices(model, j, i);
model.D{i, j} = eye(length(ind)) + model.beta*model.K{i, j} - ...
model.beta*model.K_uf(:, ind)'*model.invK_uu*model.K_uf(:, ind);
[model.Dinv{i, j}, U] = pdinv(model.D{i, j});
model.logDetD(i, j) = logdet(model.D{i, j}, U);
K_ufDinvK_uf = model.K_uf(:, ind)*model.Dinv{i, j}...
*model.K_uf(:, ind)';
model.A{j} = model.A{j} + K_ufDinvK_uf;
Dinvm{i}(ind, j) = model.Dinv{i, j}*model.m(ind, j);
K_ufDinvm(:, j) = K_ufDinvm(:, j) + model.K_uf(:, ind)*Dinvm{i}(ind, ...
j);
end
% This can become unstable when K_ufDinvK_uf is low rank.
[model.Ainv{j}, U] = pdinv(model.A{j});
model.logDetA(j) = logdet(model.A{j}, U);
end
% compute inner products
for j = 1:model.d
model.innerProducts(1, j) = - model.beta*K_ufDinvm(:, j)'*model.Ainv{j}*K_ufDinvm(:, ...
j);
end
for i = 1:length(model.blockEnd)
for j = 1:model.d
ind = gpDataIndices(model, j, i);
model.innerProducts(1, j) = model.innerProducts(1, j) ...
+ model.beta*Dinvm{i}(ind, j)'*model.m(ind, j);
end
end
end
otherwise
error('Unknown approximating criterion.')
end