Algorithm 1.

ECME algorithm to learn TD-GPFA model parameters

	Initialize θ0;
n ← 1;
repeat
	E-step: Compute P(X|Y) according to θn;
	CM-step 1: Define g1(θn) = {vec(Dn)} and maximize
	f(θn) = E[log P(X, Y|θn)] wrt θn keeping g1 (θn) fixed;
	CM-step 2: Define $g_2({\theta }^n)=\{\mathit{\text{vec}}(C^n),{\mathbf{d}}^n,\mathit{\text{diag}}(R^n),{\tau }_1^n\dots {\tau }_p^n\}$ and
	maximize L(θn) = P(Y|θn) wrt θn keeping g2(θn) fixed;
	n ← n + 1
until θn has converged or n = max number of iterations;