Hybrid random fields. A scalable approach to structure and parameter learning in probabilistic graphical models
type: Item
instance of: scholarly article
title: Hybrid random fields. A scalable approach to structure and parameter learning in probabilistic graphical models
zbMATH Open document ID: 1278.60004
DOI: 10.1007/978-3-642-20308-4
author: A. Freno
author: E. Trentin
published in: Intelligent Systems Reference Library
publication date: 2011-05-12T00:00:00Z
review text: This book presents novel probabilistic graphical models, i.e., hybrid random fields. These graphical models realize the tight binding between probability and graph theory by representing random variables as the nodes of a graph, and statistical dependencies among the variables by the graph's edges. However, the expression ``graphical model'' includes a number of learning machines, such as inductive logic programming, statistical relational learning, machine learning over structured domains, recursive neural networks, graph neural networks, etc. Before given a more precise picture of this book, it may be good to point out a number of problems presented in the text. Chapter 2 introduces the idea of Bayesian networks in a qualitative manner. The given formal definition involves hybrid random fields, namely the Markov condition, \(d\)-separation, the Markov blanket, and their relationship with the factorization of the overall, joint distribution of the variables represented by the whole network. Additionally, the chapter gives a survey on generalizations of the basic model (such as dynamic Bayesian networks and hidden Markov models). Chapter 3 provides a step-by-step introduction to the major ideas behind the concept of Markov random field, starting from stochastic processes. The role of the potential energy of local neighborhoods over an undirected graph is pointed out, along with the motivations behind the choice of modelling the overall joint density via the Gibbs distribution. Moreover, the theoretical justification for the definition of Markov random fields in the light of the equivalence between the assumption of the Gibbs distribution and the emergence of the Markov property is provided. In Chapter 4, the hybrid random field (HRF) model is introduced. The HRF model represents the joint probability distribution of its variables over a set of random variables that satisfies certain conditions involving the concepts of directed and undirected union. The chapter disc…
reviewed by: Jerzy Martyna
Mathematics Subject Classification ID: 60-02
Mathematics Subject Classification ID: 60G60
Mathematics Subject Classification ID: 62M02
Mathematics Subject Classification ID: 62F15
Mathematics Subject Classification ID: 68R10
Mathematics Subject Classification ID: 68T05
Mathematics Subject Classification ID: 05C90
zbMATH DE Number: 5887505
zbMATH Keywords: research exposition
zbMATH Keywords: probability theory
zbMATH Keywords: random fields
zbMATH Keywords: Markov processes
zbMATH Keywords: hypothesis testing
zbMATH Keywords: Bayesian inference
zbMATH Keywords: graph theory
zbMATH Keywords: learning and adaptive systems
zbMATH Keywords: applications
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-3-642-20308-4
OpenAlex ID: W2501347266
description: scientific article; zbMATH DE number 5887505