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Latent variable models (LVMs) represent observed variables by parameterizedfunctions of latent variables. Prominent examples of LVMs for unsupervisedlearning are probabilistic PCA or probabilistic SC which both assume a weightedlinear summation of the latents to determine the mean of a Gaussiandistribution for the observables. In many cases, however, observables do notfollow a Gaussian distribution. For unsupervised learning, LVMs which assumespecific non-Gaussian observables have therefore been considered. Already forspecific choices of distributions, parameter optimization is challenging andonly a few previous contributions considered LVMs with more generally definedobservable distributions. Here, we consider LVMs that are defined for a rangeof different distributions, i.e., observables can follow any (regular)distribution of the exponential family. The novel class of LVMs presented isdefined for binary latents, and it uses maximization in place of summation tolink the latents to observables. To derive an optimization procedure, we followan EM approach for maximum likelihood parameter estimation. We show that a setof very concise parameter update equations can be derived which feature thesame functional form for all exponential family distributions. The derivedgeneric optimization can consequently be applied to different types of metricdata as well as to different types of discrete data. Also, the derivedoptimization equations can be combined with a recently suggested variationalacceleration which is likewise generically applicable to the LVMs consideredhere. So, the combination maintains generic and direct applicability of thederived optimization procedure, but, crucially, enables efficient scalability.We numerically verify our analytical results and discuss some potentialapplications such as learning of variance structure, noise type estimation anddenoising.

Generic Unsupervised Optimization for a Latent Variable Model With Exponential Family Observables