Post Doctoral: Probabilistic Models for Hierarchical Neural Networks

9404932 Jordan实验科学副学士将支持麻省理工学院的一个跨学科研究项目。提出的研究将集中在概率模型的层次神经网络。将详细研究两种特定的架构：层次混合专家（HME）和玻尔兹曼树。将开发用于模拟更复杂概率过程混合的HME网络，例如隐马尔可夫链和最优观察者。来自统计学的期望最大化（EM）原则将被用于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与统计物理中的平均场理论的关系来分析。玻尔兹曼机是一类用于约束满足的概率模型，由于缺乏有效的学习算法，它的发展一直受到阻碍。具有树状结构的玻尔兹曼机具有简化的特征，使它们更快、更高效。对玻尔兹曼树的进一步研究将为监督学习和无监督学习带来更强大的算法。将解释玻尔兹曼树与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. ***