Distributed Bayesian Learning with Stochastic Naturalgradient Expectation Propagation and the Posterior Server
Abstract
This paper makes two contributions to Bayesian machine learning algorithms. Firstly, we propose stochastic natural gradient expectation propagation (SNEP), a novel alternative to expectation propagation (EP), a popular variational inference algorithm. SNEP is a black box variational algorithm, in that it does not require any simplifying assumptions on the distribution of interest, beyond the existence of some Monte Carlo sampler for estimating the moments of the EP tilted distributions. Further, as opposed to EP which has no guarantee of convergence, SNEP can be shown to be convergent, even when using Monte Carlo moment estimates. Secondly, we propose a novel architecture for distributed Bayesian learning which we call the posterior server. The posterior server allows scalable and robust Bayesian learning in cases where a data set is stored in a distributed manner across a cluster, with each compute node containing a disjoint subset of data. An independent Monte Carlo sampler is run on each compute node, with direct access only to the local data subset, but which targets an approximation to the global posterior distribution given all data across the whole cluster. This is achieved by using a distributed asynchronous implementation of SNEP to pass messages across the cluster. We demonstrate SNEP and the posterior server on distributed Bayesian learning of logistic regression and neural networks. Keywords: Distributed Learning, Large Scale Learning, Deep Learning, Bayesian Learn ing, Variational Inference, Expectation Propagation, Stochastic Approximation, Natural Gradient, Markov chain Monte Carlo, Parameter Server, Posterior Server.
 Publication:

arXiv eprints
 Pub Date:
 December 2015
 arXiv:
 arXiv:1512.09327
 Bibcode:
 2015arXiv151209327H
 Keywords:

 Computer Science  Machine Learning;
 Statistics  Machine Learning
 EPrint:
 37 pages, 7 figures