Accepted author manuscript, 450 KB, PDF document
Available under license: CC BY-NC: Creative Commons Attribution-NonCommercial 4.0 International License
Final published version
Research output: Contribution to conference - Without ISBN/ISSN › Conference paper › peer-review
Research output: Contribution to conference - Without ISBN/ISSN › Conference paper › peer-review
}
TY - CONF
T1 - Large-Scale Stochastic Sampling from the Probability Simplex
AU - Baker, Jack
AU - Fearnhead, Paul
AU - Fox, Emily B
AU - Nemeth, Christopher
PY - 2018/12/3
Y1 - 2018/12/3
N2 - 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.
AB - 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.
KW - stat.CO
KW - cs.LG
KW - stat.ML
M3 - Conference paper
SP - 6722
EP - 6732
T2 - 32nd Neural Information Processing Systems Conference (NIPS 2018)
Y2 - 3 December 2018 through 8 December 2018
ER -