2,707 research outputs found
Fixed-Form Variational Posterior Approximation through Stochastic Linear Regression
We propose a general algorithm for approximating nonstandard Bayesian
posterior distributions. The algorithm minimizes the Kullback-Leibler
divergence of an approximating distribution to the intractable posterior
distribution. Our method can be used to approximate any posterior distribution,
provided that it is given in closed form up to the proportionality constant.
The approximation can be any distribution in the exponential family or any
mixture of such distributions, which means that it can be made arbitrarily
precise. Several examples illustrate the speed and accuracy of our
approximation method in practice
Distributed Bayesian Learning with Stochastic Natural-gradient Expectation Propagation and the Posterior Server
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.Comment: 37 pages, 7 figure
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