# Context-specific independence in graphical log-linear models

arXiv: https://arxiv.org/abs/1409.2713 · HTML: https://mlsanity.com/paper/1409.2713/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Sep 2014.

## Built on by (most cited first, 3 of 3)

- [Staged trees and asymmetry-labeled DAGs](https://mlsanity.com/paper/2108.01994/) (2021)
- [Structure Learning of Contextual Markov Networks using Marginal Pseudo-likelihood](https://mlsanity.com/paper/2103.15540/) (2021)
- [Explaining Deep Tractable Probabilistic Models: The sum-product network case](https://mlsanity.com/paper/2110.09778/) (2021)

## Abstract (arXiv)

Log-linear models are the popular workhorses of analyzing contingency tables. A log-linear parameterization of an interaction model can be more expressive than a direct parameterization based on probabilities, leading to a powerful way of defining restrictions derived from marginal, conditional and context-specific independence. However, parameter estimation is often simpler under a direct parameterization, provided that the model enjoys certain decomposability properties. Here we introduce a cyclical projection algorithm for obtaining maximum likelihood estimates of log-linear parameters under an arbitrary context-specific graphical log-linear model, which needs not satisfy criteria of decomposability. We illustrate that lifting the restriction of decomposability makes the models more expressive, such that additional context-specific independencies embedded in real data can be identified. It is also shown how a context-specific graphical model can correspond to a non-hierarchical log-linear parameterization with a concise interpretation. This observation can pave way to further development of non-hierarchical log-linear models, which have been largely neglected due to their believed lack of interpretability.