Inversion of Bayesian Networks
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Abstract (arXiv)
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 local conditions for the recognition network to have the desired qualities. It turns out that for the local conditions the property perfectness (for every node, all parents are joined) plays an important role.
Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 5 of its 22 references that are in the map. First posted on arXiv 20 Dec 2022.
Builds on
5 of 22 references.
References · 5
- 2013Auto-Encoding Variational Bayescited by 4,053
- 2017Learning Sparse Neural Networks through L0 Regularizationcited by 583
- 2020Amortized Causal Discovery: Learning to Infer Causal Graphs from Time-Series Datacited by 100
- 2017Faithful Inversion of Generative Models for Effective Amortized Inferencecited by 29
- 2018Doubly Semi-Implicit Variational Inferencecited by 19
Built on by
Citing papers per year: 2023: 1.
1 paper.
- 2023On the Natural Gradient of the Evidence Lower Boundcited by 1
- 2023On the Natural Gradient of the Evidence Lower Bound20 Jul 2023