Due to the assumption of factorial posterior distribution of the models, the cost function can be computed as easily as before. Let us denote and the posterior mean and variance of by and . After having computed the posterior mean and variance of the sources, the computation of the C p part of the cost function proceeds as with nonlinear factor analysis in the previous section. The C q part yields terms of the form and we have thus reduced the problem to a previously solved one. The terms are the same as for the nonlinear factor analysis and otherwise the equation has the same form as in model selection in Chap.
Most update rules are the same as for nonlinear factor analysis.
It turns out that they both will be weighted with , i.e., the observation is used for adapting the parameters in proportion to the posterior probability of that observation originating from that particular Gaussian distribution.