{"title":"Discrete Graphical Models - An Optimization Perspective","authors":"Bogdan Savchynskyy","doi":"10.1561/0600000084","DOIUrl":null,"url":null,"abstract":"This monograph is about discrete energy minimization for discrete graphical models. It considers graphical models, or, more precisely, maximum a posteriori inference for graphical models, purely as a combinatorial optimization problem. Modeling, applications, probabilistic interpretations and many other aspects are either ignored here or find their place in examples and remarks only. It covers the integer linear programming formulation of the problem as well as its linear programming, Lagrange and Lagrange decomposition-based relaxations. In particular, it provides a detailed analysis of the polynomially solvable acyclic and submodular problems, along with the corresponding exact optimization methods. Major approximate methods, such as message passing and graph cut techniques are also described and analyzed comprehensively. The monograph can be useful for undergraduate and graduate students studying optimization or graphical models, as well as for experts in optimization who want to have a look into graphical models. To make the monograph suitable for both categories of readers we explicitly separate the mathematical optimization background chapters from those specific to graphical models.","PeriodicalId":45662,"journal":{"name":"Foundations and Trends in Computer Graphics and Vision","volume":"85 1","pages":"160-429"},"PeriodicalIF":3.8000,"publicationDate":"2019-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"23","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Foundations and Trends in Computer Graphics and Vision","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1561/0600000084","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 23
Abstract
This monograph is about discrete energy minimization for discrete graphical models. It considers graphical models, or, more precisely, maximum a posteriori inference for graphical models, purely as a combinatorial optimization problem. Modeling, applications, probabilistic interpretations and many other aspects are either ignored here or find their place in examples and remarks only. It covers the integer linear programming formulation of the problem as well as its linear programming, Lagrange and Lagrange decomposition-based relaxations. In particular, it provides a detailed analysis of the polynomially solvable acyclic and submodular problems, along with the corresponding exact optimization methods. Major approximate methods, such as message passing and graph cut techniques are also described and analyzed comprehensively. The monograph can be useful for undergraduate and graduate students studying optimization or graphical models, as well as for experts in optimization who want to have a look into graphical models. To make the monograph suitable for both categories of readers we explicitly separate the mathematical optimization background chapters from those specific to graphical models.
期刊介绍:
The growth in all aspects of research in the last decade has led to a multitude of new publications and an exponential increase in published research. Finding a way through the excellent existing literature and keeping up to date has become a major time-consuming problem. Electronic publishing has given researchers instant access to more articles than ever before. But which articles are the essential ones that should be read to understand and keep abreast with developments of any topic? To address this problem Foundations and Trends® in Computer Graphics and Vision publishes high-quality survey and tutorial monographs of the field.
Each issue of Foundations and Trends® in Computer Graphics and Vision comprises a 50-100 page monograph written by research leaders in the field. Monographs that give tutorial coverage of subjects, research retrospectives as well as survey papers that offer state-of-the-art reviews fall within the scope of the journal.