lzhbrian / mcmc

An introduction of MCMC, implementation of TAP, AIS, RTS algorithm to estimate the partition function of an RBM (Project of Stochastic Process course)

Markov Chain Monte Carlo

An overview

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• Whole paper in PDF： ./mcmc.pdf
• Source Codes in the paper can be found in this repository.

Abstract

Markov Chain Monte Carlo (MCMC) is a technique to make an estimation of a statistic by simulation in a complex model. Restricted Bolztmann Machine(RBM) is a crucial model in the field of Machine Learning. However, training a large RBM model will include intractable computation of the partition functions, i.e.Z(θ). This problem has aroused interest in the work of estimation using a MCMC methods. In this paper, we first conduct Metropolis-Hastings Algorithm, one of the most prevalent sampling methods, and analyze its correctness & performance, along with the choice of the accepting rate. We then implement three algorithms: TAP, AIS, RTS, to estimate partition functions of an RBM model. Our work not only give an introduction about the available algorithms, but systematically compare the performance & difference between them. We seek to provide an overall view in the field of MCMC.

Author

Tzu-Heng Lin is currently an undergraduate student in the Dept. of Electronic Engineering, Tsinghua University. His research interests include Big Data Mining, Machine Learning, etc. For more information about him, please see www.linkedin.com/in/lzhbrian . Feel free to contact him at any time via [email protected] or [email protected]

├── LICENSE
├── README.md
├── requirement/
├── src
│   ├── MH
│   │   ├── metropolis_hasting.R
│   └── partition
│       ├── AIS.m
│       ├── RTS.m
│       ├── TAP.m
│       ├── ais_sampling.m
│       ├── calculate_logprob.m
│       ├── draw_ais.m
│       ├── logsum.m
│       ├── main.m
│       └── run.m
├── tex/
├── upload/
└── z.mat