8,637 research outputs found
Global consensus Monte Carlo
To conduct Bayesian inference with large data sets, it is often convenient or
necessary to distribute the data across multiple machines. We consider a
likelihood function expressed as a product of terms, each associated with a
subset of the data. Inspired by global variable consensus optimisation, we
introduce an instrumental hierarchical model associating auxiliary statistical
parameters with each term, which are conditionally independent given the
top-level parameters. One of these top-level parameters controls the
unconditional strength of association between the auxiliary parameters. This
model leads to a distributed MCMC algorithm on an extended state space yielding
approximations of posterior expectations. A trade-off between computational
tractability and fidelity to the original model can be controlled by changing
the association strength in the instrumental model. We further propose the use
of a SMC sampler with a sequence of association strengths, allowing both the
automatic determination of appropriate strengths and for a bias correction
technique to be applied. In contrast to similar distributed Monte Carlo
algorithms, this approach requires few distributional assumptions. The
performance of the algorithms is illustrated with a number of simulated
examples
Patterns of Scalable Bayesian Inference
Datasets are growing not just in size but in complexity, creating a demand
for rich models and quantification of uncertainty. Bayesian methods are an
excellent fit for this demand, but scaling Bayesian inference is a challenge.
In response to this challenge, there has been considerable recent work based on
varying assumptions about model structure, underlying computational resources,
and the importance of asymptotic correctness. As a result, there is a zoo of
ideas with few clear overarching principles.
In this paper, we seek to identify unifying principles, patterns, and
intuitions for scaling Bayesian inference. We review existing work on utilizing
modern computing resources with both MCMC and variational approximation
techniques. From this taxonomy of ideas, we characterize the general principles
that have proven successful for designing scalable inference procedures and
comment on the path forward
parallelMCMCcombine: An R Package for Bayesian Methods for Big Data and Analytics
Recent advances in big data and analytics research have provided a wealth of
large data sets that are too big to be analyzed in their entirety, due to
restrictions on computer memory or storage size. New Bayesian methods have been
developed for large data sets that are only large due to large sample sizes;
these methods partition big data sets into subsets, and perform independent
Bayesian Markov chain Monte Carlo analyses on the subsets. The methods then
combine the independent subset posterior samples to estimate a posterior
density given the full data set. These approaches were shown to be effective
for Bayesian models including logistic regression models, Gaussian mixture
models and hierarchical models. Here, we introduce the R package
parallelMCMCcombine which carries out four of these techniques for combining
independent subset posterior samples. We illustrate each of the methods using a
Bayesian logistic regression model for simulation data and a Bayesian Gamma
model for real data; we also demonstrate features and capabilities of the R
package. The package assumes the user has carried out the Bayesian analysis and
has produced the independent subposterior samples outside of the package. The
methods are primarily suited to models with unknown parameters of fixed
dimension that exist in continuous parameter spaces. We envision this tool will
allow researchers to explore the various methods for their specific
applications, and will assist future progress in this rapidly developing field.Comment: for published version see:
http://www.plosone.org/article/fetchObject.action?uri=info%3Adoi%2F10.1371%2Fjournal.pone.0108425&representation=PD
Global consensus Monte Carlo
To conduct Bayesian inference with large data sets, it is often convenient or necessary to distribute the data across multiple machines. We consider a likelihood function expressed as a product of terms, each associated with a subset of the data. Inspired by global variable consensus optimisation, we introduce an instrumental hierarchical model associating auxiliary statistical parameters with each term, which are conditionally independent given the top-level parameters. One of these top-level parameters controls the unconditional strength of association between the auxiliary parameters. This model leads to a distributed MCMC algorithm on an extended state space yielding approximations of posterior expectations. A trade-off between computational tractability and fidelity to the original model can be controlled by changing the association strength in the instrumental model. We further propose the use of a SMC sampler with a sequence of association strengths, allowing both the automatic determination of appropriate strengths and for a bias correction technique to be applied. In contrast to similar distributed Monte Carlo algorithms, this approach requires few distributional assumptions. The performance of the algorithms is illustrated with a number of simulated examples
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