Discrete Graphical Models
An Optimization Perspective
Seiten
2019
now publishers Inc (Verlag)
978-1-68083-638-7 (ISBN)
now publishers Inc (Verlag)
978-1-68083-638-7 (ISBN)
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Explores discrete energy minimization for discrete graphical models. The book considers graphical models, or, more precisely, maximum a posteriori inference for graphical models, purely as a combinatorial optimization problem.
Discrete Graphical Models: An Optimization Perspective 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.
This 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.
Discrete Graphical Models: An Optimization Perspective 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.
This 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.
1. Introduction to Inference for Graphical Models
2. Acyclic Graphical Models
3. Background: (Integer) Linear Programs and Their Geometry
4. Energy Minimization as Integer Linear Program
5. Background: Basics of Convex Analysis
6. Lagrange Duality for MAP-inference
7. Background: Basics of Non-Smooth Convex Optimization
8. Subgradient and Coordinate Descent for MAP-Inference
9. Lagrange (Dual) Decomposition
10. Maximization of the Decomposition-Based Dual
11. Min-Cut/Max-Flow Based Inference
12. Relaxed Binary Energy as st-Min-Cut
Acknowledgements
References
| Erscheinungsdatum | 16.12.2019 |
|---|---|
| Reihe/Serie | Foundations and Trends® in Computer Graphics and Vision |
| Verlagsort | Hanover |
| Sprache | englisch |
| Maße | 156 x 234 mm |
| Gewicht | 400 g |
| Themenwelt | Mathematik / Informatik ► Informatik ► Grafik / Design |
| Informatik ► Theorie / Studium ► Künstliche Intelligenz / Robotik | |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| Mathematik / Informatik ► Mathematik ► Finanz- / Wirtschaftsmathematik | |
| ISBN-10 | 1-68083-638-2 / 1680836382 |
| ISBN-13 | 978-1-68083-638-7 / 9781680836387 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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