Introduction to Dual Decomposition for Inference - David Sontag; Amir Globerson; Tommi Jaakkola (Optimization for Machine Learning, 2011)
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