# Inversion of Bayesian Networks

arXiv: https://arxiv.org/abs/2212.10649 · HTML: https://mlsanity.com/paper/2212.10649/

## Key facts

- Cited by 1 papers 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 (most cited first, 5 of 5)

- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Learning Sparse Neural Networks through L0 Regularization](https://mlsanity.com/paper/1712.01312/) (2017)
- [Amortized Causal Discovery: Learning to Infer Causal Graphs from Time-Series Data](https://mlsanity.com/paper/2006.10833/) (2020)
- [Faithful Inversion of Generative Models for Effective Amortized Inference](https://mlsanity.com/paper/1712.00287/) (2017)
- [Doubly Semi-Implicit Variational Inference](https://mlsanity.com/paper/1810.02789/) (2018)

## Built on by (most cited first, 1 of 1)

- [On the Natural Gradient of the Evidence Lower Bound](https://mlsanity.com/paper/2307.11249/) (2023)

## 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.