# High-Dimensional Inference in Bayesian Networks

arXiv: https://arxiv.org/abs/2112.09217 · HTML: https://mlsanity.com/paper/2112.09217/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 49 references that are in the map.
- First posted on arXiv 16 Dec 2021.

## Builds on (most cited first, 12 of 12)

- [Causality for Machine Learning](https://mlsanity.com/paper/1911.10500/) (2019)
- [Causal Structure Learning](https://mlsanity.com/paper/1706.09141/) (2017)
- [Loopy Belief Propagation for Approximate Inference: An Empirical Study](https://mlsanity.com/paper/1301.6725/) (2013)
- [Large-scale empirical validation of Bayesian Network structure learning algorithms with noisy data](https://mlsanity.com/paper/2005.09020/) (2020)
- [Efficient Sampling and Structure Learning of Bayesian Networks](https://mlsanity.com/paper/1803.07859/) (2018)
- [Approximate Inference with Amortised MCMC](https://mlsanity.com/paper/1702.08343/) (2017)
- [Bayesian Networks in Healthcare: Distribution by Medical Condition](https://mlsanity.com/paper/2002.00224/) (2020)
- [Bayesian structure learning and sampling of Bayesian networks with the R package BiDAG](https://mlsanity.com/paper/2105.00488/) (2021)
- [Computational Advantages of Relevance Reasoning in Bayesian Belief Networks](https://mlsanity.com/paper/1302.1558/) (2013)
- [Hard and Soft EM in Bayesian Network Learning from Incomplete Data](https://mlsanity.com/paper/2012.05269/) (2020)
- [Efficient Learning of Bounded-Treewidth Bayesian Networks from Complete and Incomplete Data Sets](https://mlsanity.com/paper/1802.02468/) (2018)
- [Dynamic Blocking and Collapsing for Gibbs Sampling](https://mlsanity.com/paper/1309.6870/) (2013)

## Abstract (arXiv)

Inference of the marginal probability distribution is defined as the calculation of the probability of a subset of the variables and is relevant for handling missing data and hidden variables. While inference of the marginal probability distribution is crucial for various problems in machine learning and statistics, its exact computation is generally not feasible for categorical variables in Bayesian networks due to the NP-hardness of this task. We develop a divide-and-conquer approach using the graphical properties of Bayesian networks to split the computation of the marginal probability distribution into sub-calculations of lower dimensionality, thus reducing the overall computational complexity. Exploiting this property, we present an efficient and scalable algorithm for calculating the marginal probability distribution for categorical variables. The novel method is compared against state-of-the-art approximate inference methods in a benchmarking study, where it displays superior performance. As an immediate application, we demonstrate how our method can be used to classify incomplete data against Bayesian networks and use this approach for identifying the cancer subtype of kidney cancer patient samples.