# Markov random fields factorization with context-specific independences

Title | Markov random fields factorization with context-specific independences |

Publication Type | Report |

Year of Publication | 2013 |

Authors | Edera A, Bromberg F, Schlüter F |

Institution | arXiv.org |

Report Number | arXiv:1306.2295 |

Abstract | 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. |