# Hybrid Bayesian network discovery with latent variables by scoring multiple interventions

arXiv: https://arxiv.org/abs/2112.10574 · HTML: https://mlsanity.com/paper/2112.10574/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 59 references that are in the map.
- First posted on arXiv 20 Dec 2021.

## Builds on (most cited first, 9 of 9)

- [Learning Bayesian Networks: The Combination of Knowledge and Statistical Data](https://mlsanity.com/paper/1302.6815/) (2013)
- [Permutation-based Causal Inference Algorithms with Interventions](https://mlsanity.com/paper/1705.10220/) (2017)
- [Constraint-based Causal Discovery from Multiple Interventions over Overlapping Variable Sets](https://mlsanity.com/paper/1403.2150/) (2014)
- [Large-scale empirical validation of Bayesian Network structure learning algorithms with noisy data](https://mlsanity.com/paper/2005.09020/) (2020)
- [Ancestral Causal Inference](https://mlsanity.com/paper/1606.07035/) (2016)
- [Evaluating structure learning algorithms with a balanced scoring function](https://mlsanity.com/paper/1905.12666/) (2019)
- [An Empirical-Bayes Score for Discrete Bayesian Networks](https://mlsanity.com/paper/1605.03884/) (2016)
- [Bayesian network structure learning with causal effects in the presence of latent variables](https://mlsanity.com/paper/2005.14381/) (2020)
- [Scaling up Greedy Causal Search for Continuous Variables](https://mlsanity.com/paper/1507.07749/) (2015)

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

- [Causal discovery using dynamically requested knowledge](https://mlsanity.com/paper/2310.11154/) (2023)

## Abstract (arXiv)

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.