Timezone: »
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 the time-discretization error can dominate when we are near the boundary of the space. We demonstrate that because of this, current SGMCMC methods for the simplex struggle with sparse simplex spaces; when many of the components are close to zero. Unfortunately, many popular large-scale Bayesian models, such as network or topic models, require inference on sparse simplex spaces. To avoid the biases caused by this discretization error, we propose the stochastic Cox-Ingersoll-Ross process (SCIR), which removes all discretization error and we prove that samples from the SCIR process are asymptotically unbiased. We discuss how this idea can be extended to target other constrained spaces. Use of the SCIR 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.
Author Information
Jack Baker (Lancaster University)
Paul Fearnhead (Lancaster University)
Paul Fearnhead is Professor of Statistics at Lancaster University. He received his DPhil in Statistics from the University of Oxford in 1998; was a postdoctoral researcher at the University of Oxford until 2001; and then moved to the University of Lancaster, initially as a Lecturer in Statistics. He has worked on Monte Carlo methods within Bayesian statistics, including applications in population genetics, changepoint detection and inference for diffusions. He was awarded the Royal Statistical Society's Guy medal in Bronze in 2007, and Cambridge University's Adams Prize in 2006.
Emily Fox (University of Washington, Apple)
Christopher Nemeth (Lancaster University)
More from the Same Authors
-
2023 Poster: Learning Rate Free Bayesian Inference in Constrained Domains »
Louis Sharrock · Lester Mackey · Christopher Nemeth -
2023 Poster: Fast Online Changepoint Detection via Functional Pruning CUSUM Statistics »
Gaetano Romano · Idris A. Eckley · Paul Fearnhead · Guillem Rigaill -
2022 Poster: Continuously Tempered PDMP samplers »
Matthew Sutton · Robert Salomone · Augustin Chevallier · Paul Fearnhead -
2019 : Emily Fox »
Emily Fox -
2019 Poster: Pseudo-Extended Markov chain Monte Carlo »
Christopher Nemeth · Fredrik Lindsten · Maurizio Filippone · James Hensman -
2018 : Plenary Talk 4 »
Emily Fox -
2016 : Emily Fox. Sparse Graphs via Exchangeable Random Measures. »
Emily Fox -
2016 : Emily Fox : Functional Connectivity in MEG via Graphical Models of Time Series »
Emily Fox -
2015 : Bayesian Time Series: Structured Representations for Scalability »
Emily Fox -
2015 Poster: A Complete Recipe for Stochastic Gradient MCMC »
Yi-An Ma · Tianqi Chen · Emily Fox -
2014 Poster: Expectation-Maximization for Learning Determinantal Point Processes »
Jennifer A Gillenwater · Alex Kulesza · Emily Fox · Ben Taskar -
2014 Poster: Stochastic variational inference for hidden Markov models »
Nick Foti · Jason Xu · Dillon Laird · Emily Fox -
2013 Poster: Approximate Inference in Continuous Determinantal Processes »
Raja Hafiz Affandi · Emily Fox · Ben Taskar -
2013 Spotlight: Approximate Inference in Continuous Determinantal Processes »
Raja Hafiz Affandi · Emily Fox · Ben Taskar -
2013 Session: Oral Session 4 »
Emily Fox -
2012 Poster: Multiresolution Gaussian Processes »
Emily Fox · David B Dunson -
2012 Poster: Effective Split-Merge Monte Carlo Methods for Nonparametric Models of Sequential Data »
Michael Hughes · Emily Fox · Erik Sudderth -
2012 Tutorial: Exact Approximate Learning »
Paul Fearnhead -
2011 Workshop: Bayesian Nonparametric Methods: Hope or Hype? »
Emily Fox · Ryan Adams -
2009 Poster: Sharing Features among Dynamical Systems with Beta Processes »
Emily Fox · Erik Sudderth · Michael Jordan · Alan S Willsky -
2009 Oral: Sharing Features among Dynamical Systems with Beta Processes »
Emily Fox · Erik Sudderth · Michael Jordan · Alan S Willsky -
2008 Poster: Nonparametric Bayesian Learning of Switching Linear Dynamical Systems »
Emily Fox · Erik Sudderth · Michael Jordan · Alan S Willsky -
2008 Spotlight: Nonparametric Bayesian Learning of Switching Linear Dynamical Systems »
Emily Fox · Erik Sudderth · Michael Jordan · Alan S Willsky