van Oostrum, JesseJessevan OostrumVan Hintum, PeterPeterVan HintumAy, NihatNihatAy2023-11-022023-11-022024-01International Journal of Approximate Reasoning 164 : 109042 (2024-01)https://hdl.handle.net/11420/44037Variational autoencoders and Helmholtz machines use a recognition network (encoder) to approximate the posterior distribution of a generative model (decoder). In this paper we establish some necessary and some 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 local conditions for the recognition network to have the desired qualities. It turns out that for the local conditions the perfectness property (for every node, all parents are joined) plays an important role.en0888-613X2024Elsevierhttps://creativecommons.org/licenses/by/4.0/Amortized inferenceBayesian networksGenerative modelGraphical modelsRecognition modelVariational autoencoderVariational inferenceComputer SciencesJournal Article10.15480/882.884810.1016/j.ijar.2023.10904210.15480/882.8848Journal Article