double HierarchicalGaussianProcess::negativeTotalLogLikelihood()
{
/*This is the restricted version. For the unrestricted, make p=0
and remove the last term of loglik*/
const matrixd K = computeCorrMatrix();
const size_t n = K.size1();
const size_t p = mFeatM.size1();
matrixd L(n,n);
utils::cholesky_decompose(K,L);
matrixd KF(ublas::trans(mFeatM));
inplace_solve(L,KF,ublas::lower_tag());
matrixd FKF = prod(ublas::trans(KF),KF);
matrixd L2(p,p);
utils::cholesky_decompose(FKF,L2);
vectord Ky(mGPY);
inplace_solve(L,Ky,ublas::lower_tag());
vectord wML = prod(Ky,KF);
utils::cholesky_solve(L2,wML,ublas::lower());
vectord alpha = mGPY - prod(wML,mFeatM);
inplace_solve(L,alpha,ublas::lower_tag());
double sigma = ublas::inner_prod(alpha,alpha)/(n-p);
double loglik = .5*(n-p)*log(ublas::inner_prod(alpha,alpha))
+ utils::log_trace(L) + utils::log_trace(L2);
return loglik;
}
void StudentTProcessJeffreys::precomputePrediction()
{
size_t n = mData.getNSamples();
size_t p = mMean.nFeatures();
mKn.resize(n);
mKF = trans(mMean.mFeatM);
inplace_solve(mL,mKF,ublas::lower_tag());
matrixd FKF = prod(trans(mKF),mKF);
mL2 = FKF;
utils::cholesky_decompose(FKF,mL2);
vectord Ky(mData.mY);
inplace_solve(mL,Ky,ublas::lower_tag());
mWML = prod(Ky,mKF);
utils::cholesky_solve(mL2,mWML,ublas::lower());
mAlphaF = mData.mY - prod(mWML,mMean.mFeatM);
inplace_solve(mL,mAlphaF,ublas::lower_tag());
mSigma = inner_prod(mAlphaF,mAlphaF)/(n-p);
d_->setDof(n-p);
}
