# Stratified Graphical Models - Context-Specific Independence in Graphical Models

arXiv: https://arxiv.org/abs/1309.6415 · HTML: https://mlsanity.com/paper/1309.6415/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Sep 2013.

## Built on by (most cited first, 7 of 7)

- [Causal Effect Identification with Context-specific Independence Relations of Control Variables](https://mlsanity.com/paper/2110.12064/) (2021)
- [Structure Learning of Contextual Markov Networks using Marginal Pseudo-likelihood](https://mlsanity.com/paper/2103.15540/) (2021)
- [A Complete Decomposition of KL Error using Refined Information and Mode Interaction Selection](https://mlsanity.com/paper/2410.11964/) (2024)
- [Explaining Deep Tractable Probabilistic Models: The sum-product network case](https://mlsanity.com/paper/2110.09778/) (2021)
- [Identification and Estimation for Nonignorable Missing Data: A Data Fusion Approach](https://mlsanity.com/paper/2311.09015/) (2023)
- [Causal Modeling in Multi-Context Systems: Distinguishing Multiple Context-Specific Causal Graphs which Account for Observational Support](https://mlsanity.com/paper/2410.20405/) (2024)
- [Algebraic Signatures for Structural Learning in Probability Tensors](https://mlsanity.com/paper/2607.18817/) (2026)

## Abstract (arXiv)

Theory of graphical models has matured over more than three decades to provide the backbone for several classes of models that are used in a myriad of applications such as genetic mapping of diseases, credit risk evaluation, reliability and computer security, etc. Despite of their generic applicability and wide adoptance, the constraints imposed by undirected graphical models and Bayesian networks have also been recognized to be unnecessarily stringent under certain circumstances. This observation has led to the proposal of several generalizations that aim at more relaxed constraints by which the models can impose local or context-specific dependence structures. Here we consider an additional class of such models, termed as stratified graphical models. We develop a method for Bayesian learning of these models by deriving an analytical expression for the marginal likelihood of data under a specific subclass of decomposable stratified models. A non-reversible Markov chain Monte Carlo approach is further used to identify models that are highly supported by the posterior distribution over the model space. Our method is illustrated and compared with ordinary graphical models through application to several real and synthetic datasets.