1,920 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
A trust-region method for stochastic variational inference with applications to streaming data
Stochastic variational inference allows for fast posterior inference in
complex Bayesian models. However, the algorithm is prone to local optima which
can make the quality of the posterior approximation sensitive to the choice of
hyperparameters and initialization. We address this problem by replacing the
natural gradient step of stochastic varitional inference with a trust-region
update. We show that this leads to generally better results and reduced
sensitivity to hyperparameters. We also describe a new strategy for variational
inference on streaming data and show that here our trust-region method is
crucial for getting good performance.Comment: in Proceedings of the 32nd International Conference on Machine
Learning, 201
Automatic Differentiation Variational Inference
Probabilistic modeling is iterative. A scientist posits a simple model, fits
it to her data, refines it according to her analysis, and repeats. However,
fitting complex models to large data is a bottleneck in this process. Deriving
algorithms for new models can be both mathematically and computationally
challenging, which makes it difficult to efficiently cycle through the steps.
To this end, we develop automatic differentiation variational inference (ADVI).
Using our method, the scientist only provides a probabilistic model and a
dataset, nothing else. ADVI automatically derives an efficient variational
inference algorithm, freeing the scientist to refine and explore many models.
ADVI supports a broad class of models-no conjugacy assumptions are required. We
study ADVI across ten different models and apply it to a dataset with millions
of observations. ADVI is integrated into Stan, a probabilistic programming
system; it is available for immediate use
Uncovering latent structure in valued graphs: A variational approach
As more and more network-structured data sets are available, the statistical
analysis of valued graphs has become common place. Looking for a latent
structure is one of the many strategies used to better understand the behavior
of a network. Several methods already exist for the binary case. We present a
model-based strategy to uncover groups of nodes in valued graphs. This
framework can be used for a wide span of parametric random graphs models and
allows to include covariates. Variational tools allow us to achieve approximate
maximum likelihood estimation of the parameters of these models. We provide a
simulation study showing that our estimation method performs well over a broad
range of situations. We apply this method to analyze host--parasite interaction
networks in forest ecosystems.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS361 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Automatic Variational Inference in Stan
Variational inference is a scalable technique for approximate Bayesian
inference. Deriving variational inference algorithms requires tedious
model-specific calculations; this makes it difficult to automate. We propose an
automatic variational inference algorithm, automatic differentiation
variational inference (ADVI). The user only provides a Bayesian model and a
dataset; nothing else. We make no conjugacy assumptions and support a broad
class of models. The algorithm automatically determines an appropriate
variational family and optimizes the variational objective. We implement ADVI
in Stan (code available now), a probabilistic programming framework. We compare
ADVI to MCMC sampling across hierarchical generalized linear models,
nonconjugate matrix factorization, and a mixture model. We train the mixture
model on a quarter million images. With ADVI we can use variational inference
on any model we write in Stan
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