Algorithm 1:

The EM algorithm for estimating the hc-ICA model parameters.

Initial Values: Starting values of

{\hat{Θ}}^{(0)}

and

{\hat{β}}^{0}

are obtained using TC-GICA estimates via GIFT.

REPEAT

E Step:

1. Evaluate the conditional distribution

\tilde{p} [s (υ) | y (υ); {\hat{Θ}}^{(K)}] .

2. Evaluate the conditional expectations in

Q (Θ | {\hat{Θ}}^{(K)})

with regard to

\tilde{p} [s (υ) | y (υ); {\hat{Θ}}^{(K)}]

Q (Θ | {\hat{Θ}}^{(k)}) = \sum_{v = 1}^{V} E_{s (υ) | y (υ)} [l_{υ} (Θ; Y, X, S, Ƶ)] .

M Step:

Update parameters as follows

{\hat{Θ}}^{(k + 1)} = {a r g m a x}_{Θ} Q (Θ | {\hat{Θ}}^{(k)})

UNTIL max iterations or convergence, i.e.

\frac{‖ {\hat{Θ}}_{G}^{(k + 1)} - {\hat{Θ}}_{G}^{(k)} ‖}{‖ {\hat{Θ}}_{G}^{(k)} ‖} < ϵ_{g}

and

\frac{‖ {\hat{Θ}}_{L}^{(k + 1)} - {\hat{Θ}}_{L}^{(k)} ‖}{‖ {\hat{Θ}}_{L}^{(k)} ‖} < ϵ_{l} .