# Discovery and density estimation of latent confounders in Bayesian networks with evidence lower bound

arXiv: https://arxiv.org/abs/2206.05490 · HTML: https://mlsanity.com/paper/2206.05490/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 27 references that are in the map.
- First posted on arXiv 11 Jun 2022.

## Builds on (most cited first, 5 of 5)

- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [A survey of Bayesian Network structure learning](https://mlsanity.com/paper/2109.11415/) (2021)
- [VAEM: a Deep Generative Model for Heterogeneous Mixed Type Data](https://mlsanity.com/paper/2006.11941/) (2020)
- [Large-scale empirical validation of Bayesian Network structure learning algorithms with noisy data](https://mlsanity.com/paper/2005.09020/) (2020)
- [The Bayesian Structural EM Algorithm](https://mlsanity.com/paper/1301.7373/) (2013)

## Built on by (most cited first, 2 of 2)

- [Open problems in causal structure learning: A case study of COVID-19 in the UK](https://mlsanity.com/paper/2305.03859/) (2023)
- [Covariate Dependent Mixture of Bayesian Networks](https://mlsanity.com/paper/2501.05745/) (2025)

## Abstract (arXiv)

Discovering and parameterising latent confounders represent important and challenging problems in causal structure learning and density estimation respectively. In this paper, we focus on both discovering and learning the distribution of latent confounders. This task requires solutions that come from different areas of statistics and machine learning. We combine elements of variational Bayesian methods, expectation-maximisation, hill-climbing search, and structure learning under the assumption of causal insufficiency. We propose two learning strategies; one that maximises model selection accuracy, and another that improves computational efficiency in exchange for minor reductions in accuracy. The former strategy is suitable for small networks and the latter for moderate size networks. Both learning strategies perform well relative to existing solutions.