Hybrid Bayesian network discovery with latent variables by scoring multiple interventions

TL;DR

This paper introduces a hybrid Bayesian network structure learning algorithm that effectively incorporates observational and interventional data, handles latent variables, and improves accuracy over existing methods.

Contribution

The proposed mFGS-BS algorithm is a novel hybrid approach that combines scoring and search techniques to learn causal structures with latent confounders from multiple data sources.

Findings

Improves structure learning accuracy on benchmark networks

Handles latent variables and multiple interventions effectively

Demonstrates computational efficiency on large datasets

Abstract

In Bayesian Networks (BNs), the direction of edges is crucial for causal reasoning and inference. However, Markov equivalence class considerations mean it is not always possible to establish edge orientations, which is why many BN structure learning algorithms cannot orientate all edges from purely observational data. Moreover, latent confounders can lead to false positive edges. Relatively few methods have been proposed to address these issues. In this work, we present the hybrid mFGS-BS (majority rule and Fast Greedy equivalence Search with Bayesian Scoring) algorithm for structure learning from discrete data that involves an observational data set and one or more interventional data sets. The algorithm assumes causal insufficiency in the presence of latent variables and produces a Partial Ancestral Graph (PAG). Structure learning relies on a hybrid approach and a novel Bayesian scoring paradigm that calculates the posterior probability of each directed edge being added to the learnt graph. Experimental results based on well-known networks of up to 109 variables and 10k sample size show that mFGS-BS improves structure learning accuracy relative to the state-of-the-art and it is computationally efficient.