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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2015, Vol. 32 ›› Issue (2): 159-173.doi: 10.3969/j.issn.1005-3085.2015.02.001

• •    下一篇

受限波尔兹曼机

张春霞1,  姬楠楠2,  王冠伟3   

  1. 1- 西安交通大学数学与统计学院，西安 710049
    2- 长安大学理学院，西安 710064
    3- 西安工业大学机电工程学院，西安 710021
  • 收稿日期:2013-08-22 接受日期:2014-05-19 出版日期:2015-04-15 发布日期:2015-06-15
  • 基金资助:
    国家重点基础研究发展计划973项目 (2013CB329406)；国家自然科学基金重大研究计划 (91230101)；国家自然科学基金 (11201367)；中央高校基本科研业务费专项基金 (xjj2011048).

Restricted Boltzmann Machines

ZHANG Chun-xia1,   JI Nan-nan2,   WANG Guan-wei3   

  1. 1- School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049
    2- School of Science, Chang'an University, Xi'an 710064
    3- School of Mechatronic Engineering, Xi'an Technological University, Xi'an 710021
  • Received:2013-08-22 Accepted:2014-05-19 Online:2015-04-15 Published:2015-06-15
  • Supported by:
    The National Basic Research Program of China, 973 Program (2013CB329406); the Major Research Project of the National Natural Science Foundation of China (91230101); the National Natural Science Foundation of China (11201367); the Fundamental Research Funds for the Central Universities of China (xjj2011048).

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摘要： 受限波尔兹曼机(restricted Boltzmann machines, RBM)是一类具有两层结构、对称连接且无自反馈的随机神经网络模型，层间全连接，层内无连接．近年来，随着RBM的快速学习算法---对比散度的出现，机器学习界掀起了研究RBM理论及应用的热潮．实践表明，RBM是一种有效的特征提取方法，用于初始化前馈神经网络可明显提高泛化能力，堆叠多个RBM组成的深度信念网络能提取更抽象的特征．鉴于RBM的优点及其在深度学习中的广泛应用，本文对RBM的基本模型、学习算法、参数设置、评估方法、变形算法等进行了详细介绍，最后探讨了RBM在未来值得研究的方向．

关键词: 机器学习, 深度学习, 受限波尔兹曼机, 对比散度, Gibbs采样

Abstract:

A restricted Boltzmann machine (RBM) is a particular type of random neural network model which has two-layer architecture, symmetric connections and no self-feedback. The two layers in an RBM are fully connected but there are no connections within the same layer. Recently, with the advent of a fast learning algorithm for RBMs (i.e., contrastive divergence), the machine learning community set off a surge to study the theory and applications of RBMs since it has many advantages. For example, a RBM provides us an effective tool to detect features. When a feed-forward neural network is initialized with an RBM, its generalization capability can be significantly improved. A deep belief network composed of several RBMs can detect more abstract features. Due to the advantages and wide applications of RBMs in deep learning, this paper attempts to provide a introductory guide for novice. It presents a detailed introduction of basic RBM model, its representative learning algorithm, parametric settings, evaluation methods, its variants and etc. Finally, some research directions of RBMs that are deserved to be further studied are discussed.

Key words: machine learning, deep learning, restricted Boltzmann machine, contrastive divergence, Gibbs sampling

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