Post Doctoral: Probabilistic Models for Hierarchical Neural Networks

9404932乔丹实验科学协会将支持麻省理工学院的跨学科研究计划。建议的研究将集中在递阶神经网络的概率模型上。将详细研究两种特定的体系结构：分层专家混合(HME)和Boltzmann树。将开发对更复杂的概率过程的混合建模的HME网络，例如隐马尔可夫链和最优观测器。统计中的期望最大化(EM)原则将被用来为这些体系结构开发学习算法。这些EM算法的行为将通过利用EM与统计物理学中的平均场理论的关系来分析。Boltzmann机器是一类通用的约束满足概率模型，由于缺乏有效的学习算法，其发展一直受到阻碍。波尔兹曼机器具有树状结构，具有简化功能，使它们更快、更高效。对Boltzmann树的进一步研究将带来更强大的监督和非监督学习算法。将解释玻尔兹曼树和概率推理的信念网络之间的各种相似之处。***

9404932 Jordan The Associateship in Experimental Science will support a program of interdisciplinary research at the Massachusetts Institute of Technology. The proposed research will focus on probabilistic models for hierarchical neural networks. Two specific architectures will be studied in detail: hierarchical mixtures-of-experts (HME) and Boltzmann trees. HME networks that model mixtures of more complicated probabilistic processes, such as hidden Markov chains and optimal observers will be developed. The expectation-maximization (EM) principle from statistics will be utilized to develop learning algorithms for these architectures. The behavior of these EM algorithms will be analyzed by exploiting the relationship of EM to mean-field theories from statistical physics. Boltzmann machines are a general class of probabilistic model for constraint satisfaction whose development has been hindered by the lack of an efficient learning algorithm. Boltzmann machines with tree-like architectures have simplifying features that make them faster and more efficient. Further work on Boltzmann trees will lead to more powerful algorithms for supervised and unsupervised learning. Various parallels between Boltzmann trees and belief networks for probabilistic reasoning will be explained. ***