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Large-Scale Stochastic Sampling from the Probability Simplex

Research output: Contribution to conference - Without ISBN/ISSN Conference paper

Published
Publication date3/12/2018
Number of pages11
Pages6722-6732
Original languageEnglish
Event32nd Neural Information Processing Systems Conference (NIPS 2018) - Palais des Congrès de Montréal, Montreal, Canada
Duration: 3/12/20188/12/2018
https://nips.cc/

Conference

Conference32nd Neural Information Processing Systems Conference (NIPS 2018)
CountryCanada
CityMontreal
Period3/12/188/12/18
Internet address

Abstract

Stochastic gradient Markov chain Monte Carlo (SGMCMC) has become a popular method for scalable Bayesian inference. These methods are based on sampling a discrete-time approximation to a continuous time process, such as the Langevin diffusion. When applied to distributions defined on a constrained space, such as the simplex, the time-discretisation error can dominate when we are near the boundary of the space. We demonstrate that while current SGMCMC methods for the simplex perform well in certain cases, they struggle with sparse simplex spaces; when many of the components are close to zero. However, most popular large-scale applications of Bayesian inference on simplex spaces, such as network or topic models, are sparse. We argue that this poor performance is due to the biases of SGMCMC caused by the discretization error. To get around this, we propose the stochastic CIR process, which removes all discretization error and we prove that samples from the stochastic CIR process are asymptotically unbiased. Use of the stochastic CIR process within a SGMCMC algorithm is shown to give substantially better performance for a topic model and a Dirichlet process mixture model than existing SGMCMC approaches.