Discrete Graphical Models - An Optimization Perspective

IF 3.8 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Foundations and Trends in Computer Graphics and Vision Pub Date : 2019-12-09 DOI:10.1561/0600000084
Bogdan Savchynskyy
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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.
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离散图形模型-优化视角
本专著是关于离散图形模型的离散能量最小化。它考虑图形模型,或者更准确地说,图形模型的最大后验推理,纯粹作为组合优化问题。建模、应用、概率解释和许多其他方面在这里要么被忽略,要么只在示例和注释中找到它们的位置。它涵盖了问题的整数线性规划公式,以及它的线性规划,拉格朗日和基于拉格朗日分解的松弛。特别地,它提供了多项式可解的无环和次模问题的详细分析,以及相应的精确优化方法。对主要的近似方法,如消息传递和图切技术进行了全面的描述和分析。对于学习优化或图形模型的本科生和研究生,以及想要研究图形模型的优化专家,本专著非常有用。为了使专著适合这两类读者,我们明确地将数学优化背景章节与那些特定于图形模型的章节分开。
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来源期刊
Foundations and Trends in Computer Graphics and Vision
Foundations and Trends in Computer Graphics and Vision COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS-
CiteScore
31.20
自引率
0.00%
发文量
1
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.
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