# Context-Specific Independence in Bayesian Networks

arXiv: https://arxiv.org/abs/1302.3562 · HTML: https://mlsanity.com/paper/1302.3562/

## Key facts

- Cited by 43 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Feb 2013.

## Built on by (most cited first, 30 of 43)

- [Explaining Predictive Uncertainty with Information Theoretic Shapley Values](https://mlsanity.com/paper/2306.05724/) (2023)
- [Causal Inference Using Tractable Circuits](https://mlsanity.com/paper/2202.02891/) (2022)
- [Fine-Grained Causal Dynamics Learning with Quantization for Improving Robustness in Reinforcement Learning](https://mlsanity.com/paper/2406.03234/) (2024)
- [Context-Specific Causal Discovery for Categorical Data Using Staged Trees](https://mlsanity.com/paper/2106.04416/) (2021)
- [SkiLD: Unsupervised Skill Discovery Guided by Factor Interactions](https://mlsanity.com/paper/2410.18416/) (2024)
- [Staged trees and asymmetry-labeled DAGs](https://mlsanity.com/paper/2108.01994/) (2021)
- [Context-Specific Representation Abstraction for Deep Option Learning](https://mlsanity.com/paper/2109.09876/) (2021)
- [Causal Effect Identification with Context-specific Independence Relations of Control Variables](https://mlsanity.com/paper/2110.12064/) (2021)
- [Structural Learning of Simple Staged Trees](https://mlsanity.com/paper/2203.04390/) (2022)
- [Highly Efficient Structural Learning of Sparse Staged Trees](https://mlsanity.com/paper/2206.06970/) (2022)
- [Causal Imitability Under Context-Specific Independence Relations](https://mlsanity.com/paper/2306.00585/) (2023)
- [Efficient Monte Carlo Tree Search via On-the-Fly State-Conditioned Action Abstraction](https://mlsanity.com/paper/2406.00614/) (2024)
- [Pointwise Mutual Information as a Performance Gauge for Retrieval-Augmented Generation](https://mlsanity.com/paper/2411.07773/) (2024)
- [Null Counterfactual Factor Interactions for Goal-Conditioned Reinforcement Learning](https://mlsanity.com/paper/2505.03172/) (2025)
- [Automated Discovery of Functional Actual Causes in Complex Environments](https://mlsanity.com/paper/2404.10883/) (2024)
- [On Discovery of Local Independence over Continuous Variables via Neural Contextual Decomposition](https://mlsanity.com/paper/2405.07220/) (2024)
- [Graphical Models with Attention for Context-Specific Independence and an Application to Perceptual Grouping](https://mlsanity.com/paper/2112.03371/) (2021)
- [cegpy: Modelling with Chain Event Graphs in Python](https://mlsanity.com/paper/2211.11366/) (2022)
- [On the Expressive Power of Tree-Structured Probabilistic Circuits](https://mlsanity.com/paper/2410.05465/) (2024)
- [Algorithmic causal structure emerging through compression](https://mlsanity.com/paper/2502.04210/) (2025)
- [Structure Learning of Contextual Markov Networks using Marginal Pseudo-likelihood](https://mlsanity.com/paper/2103.15540/) (2021)
- [Scalable Bayesian Network Structure Learning with Splines](https://mlsanity.com/paper/2110.14626/) (2021)
- [Influence-Augmented Local Simulators: A Scalable Solution for Fast Deep RL in Large Networked Systems](https://mlsanity.com/paper/2202.01534/) (2022)
- [Learning and interpreting asymmetry-labeled DAGs: a case study on COVID-19 fear](https://mlsanity.com/paper/2301.00629/) (2023)
- [Context-Specific Likelihood Weighting](https://mlsanity.com/paper/2101.09791/) (2021)
- [Explaining Deep Tractable Probabilistic Models: The sum-product network case](https://mlsanity.com/paper/2110.09778/) (2021)
- [flip-hoisting: Exploiting Repeated Parameters in Discrete Probabilistic Programs](https://mlsanity.com/paper/2110.10284/) (2021)
- [NOTMAD: Estimating Bayesian Networks with Sample-Specific Structures and Parameters](https://mlsanity.com/paper/2111.01104/) (2021)
- [Principled Diverse Counterfactuals in Multilinear Models](https://mlsanity.com/paper/2201.06467/) (2022)
- [The diameter of a stochastic matrix: A new measure for sensitivity analysis in Bayesian networks](https://mlsanity.com/paper/2407.04667/) (2024)

## Abstract (arXiv)

Bayesian networks provide a language for qualitatively representing the conditional independence properties of a distribution. This allows a natural and compact representation of the distribution, eases knowledge acquisition, and supports effective inference algorithms. It is well-known, however, that there are certain independencies that we cannot capture qualitatively within the Bayesian network structure: independencies that hold only in certain contexts, i.e., given a specific assignment of values to certain variables. In this paper, we propose a formal notion of context-specific independence (CSI), based on regularities in the conditional probability tables (CPTs) at a node. We present a technique, analogous to (and based on) d-separation, for determining when such independence holds in a given network. We then focus on a particular qualitative representation scheme - tree-structured CPTs - for capturing CSI. We suggest ways in which this representation can be used to support effective inference algorithms. In particular, we present a structural decomposition of the resulting network which can improve the performance of clustering algorithms, and an alternative algorithm based on cutset conditioning.