Reasoning and Decisions in Probabilistic Graphical Models -- A Unified Framework

摘要: Author(s): Liu, Qiang | Advisor(s): Ihler, Alexander Abstract: Probabilistic graphical models such as Markov random fields, Bayesian networks and decision (a.k.a. influence diagrams) provide powerful frameworks for representing exploiting dependence structures in complex systems. However, making predictions or decisions using involve challenging computational problems of optimization and/or estimation high dimensional spaces. These include combinatorial tasks maximum a posteriori (MAP), which finds the most likely configuration, marginalization that calculate normalization constants marginal probabilities. Even more require hybrid both: MAP find optimal prediction while marginalizing over missing information latent variables, decision-making search policies single- multi-agent systems, order to maximize expected utility uncertain environments.All these are generally NP-hard, creating need efficient approximations. The last two decades have witnessed significant progress on traditional problems, especially via development variational message passing algorithms. there has been less problems.This thesis presents unified representation all problems. Based our framework, we derive class algorithms combines advantages several existing algorithms, resulting improved performance tasks. More importantly, framework allows us easily extend inference tasks, significantly improves ability solve difficult In particular, propose spectrum belief propagation style with "message passing" forms, simple, fast amenable parallel distributed computation. We also set convergent based proximal point methods, nice form transforming problem into sequence standard show outperform approaches terms both empirical theoretical properties.