Inversion of Bayesian Networks. (arXiv:2212.10649v2 [cs.LG] UPDATED)

Variational autoencoders and Helmholtz machines use a recognition network
(encoder) to approximate the posterior distribution of a generative model
(decoder). In this paper we study the necessary and sufficient properties of a
recognition network so that it can model the true posterior distribution
exactly. These results are derived in the general context of probabilistic
graphical modelling / Bayesian networks, for which the network represents a set
of conditional independence statements. We derive both global conditions, in
terms of d-separation, and …

arxiv autoencoders bayesian context decoder distribution encoder general generative machines network networks paper posterior recognition study true variational autoencoders