Approximation Methods for Inference, Learning and Decision-Making

图形模型已成为概率推理、学习和决策领域跨学科研究的一个统一焦点。在贝叶斯网络、马尔可夫随机场、影响图、决策网络或结构化随机系统的各种设置中，图形模型形式主义足以涵盖人工智能和工程中的各种经典概率系统，同时为设计新系统提供坚实的数学基础。本研究将侧重于大规模问题的近似算法，以提供对图形模型更深入的经验和理论理解。该方法将基于概率传播，变分和蒙特卡罗方法进行推理，学习和决策，目的是了解这些方法适用的图形模型类型。PI将扩展近似方法的范围，包括混合图形模型和决策网络，并为它们提供理论收敛分析和误差分析。他还将在标准基准测试和各种应用领域中对新方法进行经验测试。研究的最终目标是建立概率图形模型作为一个成熟的工程学科，能够为推理，学习和决策中的大规模问题提供鲁棒，系统的解决方案。一个成功的图形模型近似方法将允许工程师设计一个图形解决方案，以满足给定问题的性能规范，这些规范是根据时间/精度权衡和估计/近似权衡给出的。即使朝着这些目标取得部分进展，也会对使用大规模概率系统的领域产生广泛影响，包括信息检索、医学诊断、生物序列分析、源和错误控制编码、语音识别和机器视觉

Graphical models have become a unifying focus for interdisciplinary research in the areas of probabilistic inference, learning and decision-making. Referred to in various settings as Bayesian networks, Markov random fields, influence diagrams, decision networks, or structured stochastic systems, the graphical model formalism is general enough to encompass a wide variety of classical probabilistic systems in AI and engineering, while providing a firm mathematical foundation on which to design new systems. This research will focus on approximation algorithms for large-scale problems to provide a significantly deeper empirical and theoretical understanding of graphical models. The approach will be based on probability propagation, variational and Monte Carlo methods for inference, learning and decision-making, the aim being to understand the kinds of graphical models for which these methods are appropriate. The PI will extend the scope of approximation methodology to include hybrid graphical models and decision networks, and to provide theoretical convergence analyses and error analyses for them. He will also test out the new methods empirically on standard benchmarks and in a variety of application areas. The ultimate goal of the research is to establish probabilistic graphical models as a full-fledged engineering discipline capable of providing robust, systematic solutions to large-scale problems in inference, learning and decision-making. A successful approximation methodology for graphical models would allow an engineer to design a graphical solution to meet performance specifications for a given problem, where these specifications are given in terms of time / accuracy tradeoffs and estimation / approximation tradeoffs. Even partial progress towards these goals will have wide impact in fields where large-scale probabilistic systems are used, including information retrieval, medical diagnosis, biological sequence analysis, source and error-control coding, speech recognition, and machine vision