This isn't necessarily a recent development either. I tried to reproduce Ghahramani's factorial HMM* directly from his 1997 paper, and ran into the same problem

This isn't necessarily a recent development either. I tried to reproduce Ghahramani's factorial HMM* directly from his 1997 paper, and ran into the same problem as the other implementation I found (basically, exploding mean field values or ill-conditioned covariance matrices). By luck, I managed to find his original Matlab code and discovered he used a few small hacks (mostly re-scaling and reconditioning various values) to get it all to work. I have no problem with that, but I simply cannot understand why you would omit these from the paper (though I can think of one reason - because it ruins your elegant algebra). There is no way anyone would be able to reproduce his results if the code disappeared. https://github.com/nmfisher/fhmm_julia/blob/master/structured_vfhmm2.jl https://github.com/nmfisher/fhmm_julia/blob/master/structure...