Slow mixing for Latent Dirichlet Allocation
Journal article, 2017

Markov chain Monte Carlo (MCMC) algorithms are ubiquitous in probability theory in general and in machine learning in particular. A Markov chain is devised so that its stationary distribution is some probability distribution of interest. Then one samples from the given distribution by running the Markov chain for a “long time” until it appears to be stationary and then collects the sample. However these chains are often very complex and there are no theoretical guarantees that stationarity is actually reached. In this paper we study the Gibbs sampler of the posterior distribution of a very simple case of Latent Dirichlet Allocation, an attractive Bayesian unsupervised learning model for text generation and text classification. It turns out that in some situations, the mixing time of the Gibbs sampler is exponential in the length of documents and so it is practically impossible to properly sample from the posterior when documents are sufficiently long.

MCMC

Topic model

Mixing time

Gibbs sampler

Author

Johan Jonasson

University of Gothenburg

Chalmers, Mathematical Sciences, Analysis and Probability Theory

Statistics and Probability Letters

0167-7152 (ISSN)

Vol. 129 96-100

Subject Categories

Probability Theory and Statistics

DOI

10.1016/j.spl.2017.05.011

More information

Created

10/7/2017