1,302 research outputs found
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
Exploiting the Statistics of Learning and Inference
When dealing with datasets containing a billion instances or with simulations
that require a supercomputer to execute, computational resources become part of
the equation. We can improve the efficiency of learning and inference by
exploiting their inherent statistical nature. We propose algorithms that
exploit the redundancy of data relative to a model by subsampling data-cases
for every update and reasoning about the uncertainty created in this process.
In the context of learning we propose to test for the probability that a
stochastically estimated gradient points more than 180 degrees in the wrong
direction. In the context of MCMC sampling we use stochastic gradients to
improve the efficiency of MCMC updates, and hypothesis tests based on adaptive
mini-batches to decide whether to accept or reject a proposed parameter update.
Finally, we argue that in the context of likelihood free MCMC one needs to
store all the information revealed by all simulations, for instance in a
Gaussian process. We conclude that Bayesian methods will remain to play a
crucial role in the era of big data and big simulations, but only if we
overcome a number of computational challenges.Comment: Proceedings of the NIPS workshop on "Probabilistic Models for Big
Data
PASS-GLM: polynomial approximate sufficient statistics for scalable Bayesian GLM inference
Generalized linear models (GLMs) -- such as logistic regression, Poisson
regression, and robust regression -- provide interpretable models for diverse
data types. Probabilistic approaches, particularly Bayesian ones, allow
coherent estimates of uncertainty, incorporation of prior information, and
sharing of power across experiments via hierarchical models. In practice,
however, the approximate Bayesian methods necessary for inference have either
failed to scale to large data sets or failed to provide theoretical guarantees
on the quality of inference. We propose a new approach based on constructing
polynomial approximate sufficient statistics for GLMs (PASS-GLM). We
demonstrate that our method admits a simple algorithm as well as trivial
streaming and distributed extensions that do not compound error across
computations. We provide theoretical guarantees on the quality of point (MAP)
estimates, the approximate posterior, and posterior mean and uncertainty
estimates. We validate our approach empirically in the case of logistic
regression using a quadratic approximation and show competitive performance
with stochastic gradient descent, MCMC, and the Laplace approximation in terms
of speed and multiple measures of accuracy -- including on an advertising data
set with 40 million data points and 20,000 covariates.Comment: In Proceedings of the 31st Annual Conference on Neural Information
Processing Systems (NIPS 2017). v3: corrected typos in Appendix
Federated Variational Inference Methods for Structured Latent Variable Models
Federated learning methods enable model training across distributed data
sources without data leaving their original locations and have gained
increasing interest in various fields. However, existing approaches are
limited, excluding many structured probabilistic models. We present a general
and elegant solution based on structured variational inference, widely used in
Bayesian machine learning, adapted for the federated setting. Additionally, we
provide a communication-efficient variant analogous to the canonical FedAvg
algorithm. The proposed algorithms' effectiveness is demonstrated, and their
performance is compared with hierarchical Bayesian neural networks and topic
models
- …