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基于动态Gibbs采样的RBM训练算法研究

李飞 高晓光 万开方

李飞, 高晓光, 万开方. 基于动态Gibbs采样的RBM训练算法研究. 自动化学报, 2016, 42(6): 931-942. doi: 10.16383/j.aas.2016.c150645
引用本文: 李飞, 高晓光, 万开方. 基于动态Gibbs采样的RBM训练算法研究. 自动化学报, 2016, 42(6): 931-942. doi: 10.16383/j.aas.2016.c150645
LI Fei, GAO Xiao-Guang, WAN Kai-Fang. Research on RBM Training Algorithm with Dynamic Gibbs Sampling. ACTA AUTOMATICA SINICA, 2016, 42(6): 931-942. doi: 10.16383/j.aas.2016.c150645
Citation: LI Fei, GAO Xiao-Guang, WAN Kai-Fang. Research on RBM Training Algorithm with Dynamic Gibbs Sampling. ACTA AUTOMATICA SINICA, 2016, 42(6): 931-942. doi: 10.16383/j.aas.2016.c150645

基于动态Gibbs采样的RBM训练算法研究

doi: 10.16383/j.aas.2016.c150645
基金项目: 

国家自然科学基金 61305133,61573285

详细信息
    作者简介:

    李飞 西北工业大学电子信息学院博士研究生. 2011年获得西北工业大学系统工程专业学士学位. 主要研究方向为机器学习和深度学习. E-mail: nwpulf@mail.nwpu.edu.cn

    万开方 西北工业大学电子信息学院博士研究生. 2010年获得西北工业大学系统工程专业学士学位. 主要研究方向为航空火力控制. E-mail: yibai 2003@126.com

    通讯作者:

    高晓光 西北工业大学电子信息学院教授. 1989年获得西北工业大学飞行器导航与控制系统博士学位. 主要研究方向为贝叶斯和航空火力控制. 本文通信作者. E-mail: cxg2012@nwpu.edu.cn

Research on RBM Training Algorithm with Dynamic Gibbs Sampling

Funds: 

Supported by National Natural Science Foundation of China 61305133,61573285

More Information
    Author Bio:

    LI Fei Ph. D. candidate at the School of Electronics and Information, Northwestern Polytechnical University. He received his bachelor degree in system engineering from Northwestern Polytechnical University in 2011. His re-search interest covers machine learning and deep learning.

    WAN Kai-Fang Ph. D. candidate at the School of Electronics and In-formation, Northwestern Polytechnical University. He received his bachelor degree in system en-gineering from Northwestern Polytechnical University in 2010. His main research interest is airborne ¯re control.

    Corresponding author: GAO Xiao-Guang Professor at the School of Electronics and Informa- tion, Northwestern Polytechnical Uni- versity. She received her Ph. D. degree in aircraft naviga- tion and control system from Northwestern Polytechnical University in 1989. Her research interest covers Bayes and airborne ¯re control. Corresponding author of this paper. E-mail: cxg2012@nwpu.edu.cn
  • 摘要: 目前大部分受限玻尔兹曼机(Restricted Boltzmann machines, RBMs)训练算法都是以多步Gibbs采样为基础的采样算法. 本文针对多步Gibbs采样过程中出现的采样发散和训练速度过慢的问题,首先, 对问题进行实验描述,给出了问题的具体形式; 然后, 从马尔科夫采样的角度对多步Gibbs采样的收敛性质进行了理论分析, 证明了多步Gibbs采样在受限玻尔兹曼机训练初期较差的收敛性质是造成采样发散和训练速度过慢的主要原因; 最后, 提出了动态Gibbs采样算法,给出了对比仿真实验.实验结果表明, 动态Gibbs采样算法可以有效地克服采样发散的问题,并且能够以微小的运行时间为代价获得更高的训练精度.
  • 图  1  RBM 结构

    Fig.  1  Con¯guration of RBM

    图  2  原始数据灰度图

    Fig.  2  Gray image of initial data

    图  3  重构误差图

    Fig.  3  Reconstruction error diagram

    图  4  运行时间图

    Fig.  4  Runtime diagram

    图  5  CD_1 采样灰度图

    Fig.  5  Gray image of CD_1 sampling

    图  6  CD_5 采样灰度图

    Fig.  6  Gray image of CD_5 sampling

    图  7  CD_10 采样灰度图

    Fig.  7  Gray image of CD_10 sampling

    图  8  CD_100 采样灰度图

    Fig.  8  Gray image of CD_100 sampling

    图  9  CD_500 采样灰度图

    Fig.  9  Gray image of CD_500 sampling

    图  10  CD_1000 采样灰度图

    Fig.  10  Gray image of CD_1000 sampling

    图  11  CD_500 采样灰度图

    Fig.  11  Gray image of CD_500 sampling

    图  12  CD_1000 采样灰度图

    Fig.  12  Gray image of CD_1000 sampling

    图  13  CD_500 采样灰度图

    Fig.  13  Gray image of CD_500 sampling

    图  14  CD_1000 采样灰度图

    Fig.  14  Gray image of CD_1000 sampling

    图  15  采样误差局部放大图

    Fig.  15  Local enlarged drawing of reconstruction error in initial phase

    图  16  CD_1000 采样误差局部放大图

    Fig.  16  Local enlarged drawing of reconstruction error in later stage

    图  17  重构误差对比图

    Fig.  17  Contrast of reconstruction error

    图  18  训练初期局部放大图

    Fig.  18  Local enlarged drawing of reconstruction error in initial phase

    图  19  训练后期局部放大图

    Fig.  19  Local enlarged drawing of reconstruction error in later stage

    图  20  运行时间对比图

    Fig.  20  Contrast of runtime

    图  21  运行时间对比图

    Fig.  21  Contrast of runtime

    图  22  运行时间对比图

    Fig.  22  Contrast of runtime

    图  23  运行时间对比图

    Fig.  23  Contrast of runtime

    图  24  DGS 迭代10次采样灰度图

    Fig.  24  Gray image of DGS by 10 iterations

    图  25  DGS 迭代20次采样灰度图

    Fig.  25  Gray image of DGS by 20 iterations

    图  26  DGS 迭代30次采样灰度图

    Fig.  26  Gray image of DGS by 30 iterations

    图  27  DGS 迭代40次采样灰度图

    Fig.  27  Gray image of DGS by 40 iterations

    图  28  DGS 迭代50次采样灰度图

    Fig.  28  Gray image of DGS by 50 iterations

    图  29  DGS 重构灰度图

    Fig.  29  Gray image of DGS

    表  1  网络参数初值

    Table  1  Initial value of parameters

    网络参数初始值
    a zeros(1, 784)
    b zeros(1, 500)
    w 0.1 × randn(784, 500)
    η 0.1
    下载: 导出CSV

    表  2  实验分组

    Table  2  Experimental grouping

    数据集算法迭代次数
    MNIST CD_11000
    MNIST CD_51000
    MNIST CD_101000
    MNIST CD_1001000
    MNIST CD_5001000
    MNIST CD_10001000
    下载: 导出CSV

    表  3  实验分组

    Table  3  Experimental grouping

    数据集训练算法Iter
    MNIST CD_11000
    MNIST CD_51000
    MNIST CD_101000
    MNIST CD_1001000
    MNIST CD_5001000
    MNIST CD_10001000
    MNIST DGS1000
    下载: 导出CSV

    表  4  网络参数初值

    Table  4  Initial values of parameters

    算法参数CD_k DGS
    a zeros(1,784) zeros(1,784)
    b zeros(1,500) zeros(1,500)
    w 0.1 × randn(784,500) 0.1 × randn(784,500)
    η0.10.1
    V784784
    H500500
    下载: 导出CSV

    表  5  DGS 迭代策略

    Table  5  Iterative strategy of DGS

    M Gibbs_N
    (1:m1) = (1:300) Gibbs_N1 = 1
    (m1:m2) = (300:900) Gibbs_N2 = 5
    (m2:Iter) = (900:1000) Gibbs_N3 = 10
    下载: 导出CSV
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出版历程
  • 收稿日期:  2015-10-19
  • 录用日期:  2016-05-03
  • 刊出日期:  2016-06-20

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