2013/06/10 by Alejandro Edera, Edera, Alejandro, Facundo Bromberg +3
Computer Science · #Artificial Intelligence (cs.AI) #Bayesian Methods and Mixture Models #Bayesian Modeling and Causal Inference #Data Management and Algorithms #FOS: Computer and information sciences #Machine Learning (cs.LG)
paper · pdf · doi:10.48550/arxiv.1306.2295
openalex publication_date 2013/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Markov random fields provide a compact representation of joint probability distributions by representing its independence properties in an undirected graph. The well-known Hammersley-Clifford theorem uses these conditional independences to factorize a Gibbs distribution into a set of factors. However, an important issue of using a graph to represent independences is that it cannot encode some types of independence relations, such as the context-specific independences (CSIs). They are a particular case of conditional independences that is true only for a certain assignment of its conditioning set; in contrast to conditional independences that must hold for all its assignments. This work presents a method for factorizing a Markov random field according to CSIs present in a distribution, and formally guarantees that this factorization is correct. This is presented in our main contribution, the context-specific Hammersley-Clifford theorem, a generalization to CSIs of the Hammersley-Clifford theorem that applies for conditional independences.