Contextual Symmetries in Probabilistic Graphical Models
نویسندگان
چکیده
An important approach for efficient inference in probabilistic graphical models exploits symmetries among objects in the domain. Symmetric variables (states) are collapsed into meta-variables (metastates) and inference algorithms are run over the lifted graphical model instead of the flat one. Our paper extends existing definitions of symmetry by introducing the novel notion of contextual symmetry. Two states that are not globally symmetric, can be contextually symmetric under some specific assignment to a subset of variables, referred to as the context variables. Contextual symmetry subsumes previous symmetry definitions and can represent a large class of symmetries not representable earlier. We show how to compute contextual symmetries by reducing it to the problem of graph isomorphism. We extend previous work on exploiting symmetries in the MCMC framework to the case of contextual symmetries. Our experiments on several domains of interest demonstrate that exploiting contextual symmetries can result in significant computational gains.
منابع مشابه
Markov Chains on Orbits of Permutation Groups
We present a novel approach to detecting and utilizing symmetries in probabilistic graphical models with two main contributions. First, we present a scalable approach to computing generating sets of permutation groups representing the symmetries of graphical models. Second, we introduce orbital Markov chains, a novel family of Markov chains leveraging model symmetries to reduce mixing times. We...
متن کاملLifted Probabilistic Inference
Many AI problems arising in a wide variety of fields such as machine learning, semantic web, network communication, computer vision, and robotics can elegantly be encoded and solved using probabilistic graphical models. Often, however, we are facing inference problems with symmetries and redundancies only implicitly captured in the graph structure and, hence, not exploitable by efficient infere...
متن کاملRule-based joint fuzzy and probabilistic networks
One of the important challenges in Graphical models is the problem of dealing with the uncertainties in the problem. Among graphical networks, fuzzy cognitive map is only capable of modeling fuzzy uncertainty and the Bayesian network is only capable of modeling probabilistic uncertainty. In many real issues, we are faced with both fuzzy and probabilistic uncertainties. In these cases, the propo...
متن کاملLifted Probabilistic Inference for Asymmetric Graphical Models
Lifted probabilistic inference algorithms have been successfully applied to a large number of symmetric graphical models. Unfortunately, the majority of realworld graphical models is asymmetric. This is even the case for relational representations when evidence is given. Therefore, more recent work in the community moved to making the models symmetric and then applying existing lifted inference...
متن کاملUPGMpp: a Software Library for Contextual Object Recognition
Object recognition is a cornerstone task towards the scene understanding problem. Recent works in the field boost their performance by incorporating contextual information to the traditional use of the objects’ geometry and/or appearance. These contextual cues are usually modeled through Conditional Random Fields (CRFs), a particular type of undirected Probabilistic Graphical Model (PGM), and a...
متن کامل