Introduction to Dual Decomposition for Inference

• Published in: Optimization for Machine Learning p. 219
• Main Authors: David Sontag, Amir Globerson, Tommi Jaakkola
• Format: Book Chapter
• Language: English
• Published: United States The MIT Press 30.09.2011; MIT Press
• Subjects: Acids; Algorithms; Amino acids; Applied sciences; Approximation; Artificial Intelligence; Behavioral sciences; Cartography; Chemical compounds; Chemicals; Chemistry; Classical mechanics; Cognitive processes; Cognitive psychology; Computer Science; Constrained optimization; Earth sciences; Equations of motion; Geodesy; Geography; Harmonic functions; Inference; Kinematics; Lagrange multipliers; Lagrangian function; Language; Lexicology; Linguistics; Machine Learning & Neural Networks; Mathematical optimization; Mathematical physics; Mathematical procedures; Mathematics; Mechanics; Modeling; Physical sciences; Physics; Potential theory; Probabilistic modeling; Psychology; Reasoning; Research methods; Thought processes; Words
• ISBN: 026201646X; 9780262016469
• DOI: 10.7551/mitpress/8996.003.0010

Many problems in engineering and the sciences require solutions to challenging combinatorial optimization problems. These include traditional problems such as scheduling, planning, fault diagnosis, or searching for molecular conformations. In addition, a wealth of combinatorial problems arise directly from probabilistic modeling (graphical models). Graphical models (Koller and Friedman, 2009) have been widely adopted in areas such as computational biology, machine vision, and natural language processing, and are increasingly being used as frameworks expressing combinatorial problems. Consider, for example, a protein side-chain placement problem where the goal is to find the minimum energy conformation of amino acid sidechains along a fixed