# Labeled Directed Acyclic Graphs: a generalization of context-specific independence in directed graphical models

arXiv: https://arxiv.org/abs/1310.1187 · HTML: https://mlsanity.com/paper/1310.1187/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Oct 2013.

## Built on by (most cited first, 15 of 15)

- [Context-Specific Causal Discovery for Categorical Data Using Staged Trees](https://mlsanity.com/paper/2106.04416/) (2021)
- [Staged trees and asymmetry-labeled DAGs](https://mlsanity.com/paper/2108.01994/) (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)
- [Causal Imitability Under Context-Specific Independence Relations](https://mlsanity.com/paper/2306.00585/) (2023)
- [On Discovery of Local Independence over Continuous Variables via Neural Contextual Decomposition](https://mlsanity.com/paper/2405.07220/) (2024)
- [Structure Learning of Contextual Markov Networks using Marginal Pseudo-likelihood](https://mlsanity.com/paper/2103.15540/) (2021)
- [Learning and interpreting asymmetry-labeled DAGs: a case study on COVID-19 fear](https://mlsanity.com/paper/2301.00629/) (2023)
- [NOTMAD: Estimating Bayesian Networks with Sample-Specific Structures and Parameters](https://mlsanity.com/paper/2111.01104/) (2021)
- [The diameter of a stochastic matrix: A new measure for sensitivity analysis in Bayesian networks](https://mlsanity.com/paper/2407.04667/) (2024)
- [Causal Modeling in Multi-Context Systems: Distinguishing Multiple Context-Specific Causal Graphs which Account for Observational Support](https://mlsanity.com/paper/2410.20405/) (2024)
- [Estimating Treatment Effects in Networks under Unknown Exposure Mappings](https://mlsanity.com/paper/2510.21457/) (2025)
- [Scalable Structure Learning for Sparse Context-Specific Systems](https://mlsanity.com/paper/2402.07762/) (2024)
- [stCEG: An R Package for Modelling Events over Spatial Areas Using Chain Event Graphs](https://mlsanity.com/paper/2507.06726/) (2025)
- [On the Granularity of Causal Effect Identifiability](https://mlsanity.com/paper/2510.16703/) (2025)

## Abstract (arXiv)

We introduce a novel class of labeled directed acyclic graph (LDAG) models for finite sets of discrete variables. LDAGs generalize earlier proposals for allowing local structures in the conditional probability distribution of a node, such that unrestricted label sets determine which edges can be deleted from the underlying directed acyclic graph (DAG) for a given context. Several properties of these models are derived, including a generalization of the concept of Markov equivalence classes. Efficient Bayesian learning of LDAGs is enabled by introducing an LDAG-based factorization of the Dirichlet prior for the model parameters, such that the marginal likelihood can be calculated analytically. In addition, we develop a novel prior distribution for the model structures that can appropriately penalize a model for its labeling complexity. A non-reversible Markov chain Monte Carlo algorithm combined with a greedy hill climbing approach is used for illustrating the useful properties of LDAG models for both real and synthetic data sets.