134 research outputs found
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
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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