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

TL;DR

This paper introduces methods for discovering and estimating the distribution of latent confounders in Bayesian networks, combining variational Bayesian, EM, and search techniques to improve accuracy and efficiency.

Contribution

It proposes two novel learning strategies for latent confounders that balance accuracy and computational efficiency, advancing causal structure learning.

Findings

Both strategies outperform existing solutions in accuracy.

The methods are effective for small and moderate-sized networks.

The approaches integrate multiple statistical techniques for improved results.

Abstract

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.