35,199 research outputs found
Stochastic Collapsed Variational Inference for Sequential Data
Stochastic variational inference for collapsed models has recently been
successfully applied to large scale topic modelling. In this paper, we propose
a stochastic collapsed variational inference algorithm in the sequential data
setting. Our algorithm is applicable to both finite hidden Markov models and
hierarchical Dirichlet process hidden Markov models, and to any datasets
generated by emission distributions in the exponential family. Our experiment
results on two discrete datasets show that our inference is both more efficient
and more accurate than its uncollapsed version, stochastic variational
inference.Comment: NIPS Workshop on Advances in Approximate Bayesian Inference, 201
Hierarchical Implicit Models and Likelihood-Free Variational Inference
Implicit probabilistic models are a flexible class of models defined by a
simulation process for data. They form the basis for theories which encompass
our understanding of the physical world. Despite this fundamental nature, the
use of implicit models remains limited due to challenges in specifying complex
latent structure in them, and in performing inferences in such models with
large data sets. In this paper, we first introduce hierarchical implicit models
(HIMs). HIMs combine the idea of implicit densities with hierarchical Bayesian
modeling, thereby defining models via simulators of data with rich hidden
structure. Next, we develop likelihood-free variational inference (LFVI), a
scalable variational inference algorithm for HIMs. Key to LFVI is specifying a
variational family that is also implicit. This matches the model's flexibility
and allows for accurate approximation of the posterior. We demonstrate diverse
applications: a large-scale physical simulator for predator-prey populations in
ecology; a Bayesian generative adversarial network for discrete data; and a
deep implicit model for text generation.Comment: Appears in Neural Information Processing Systems, 201
Stochastic Variational Inference
We develop stochastic variational inference, a scalable algorithm for
approximating posterior distributions. We develop this technique for a large
class of probabilistic models and we demonstrate it with two probabilistic
topic models, latent Dirichlet allocation and the hierarchical Dirichlet
process topic model. Using stochastic variational inference, we analyze several
large collections of documents: 300K articles from Nature, 1.8M articles from
The New York Times, and 3.8M articles from Wikipedia. Stochastic inference can
easily handle data sets of this size and outperforms traditional variational
inference, which can only handle a smaller subset. (We also show that the
Bayesian nonparametric topic model outperforms its parametric counterpart.)
Stochastic variational inference lets us apply complex Bayesian models to
massive data sets
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
Variational Inference in Nonconjugate Models
Mean-field variational methods are widely used for approximate posterior
inference in many probabilistic models. In a typical application, mean-field
methods approximately compute the posterior with a coordinate-ascent
optimization algorithm. When the model is conditionally conjugate, the
coordinate updates are easily derived and in closed form. However, many models
of interest---like the correlated topic model and Bayesian logistic
regression---are nonconjuate. In these models, mean-field methods cannot be
directly applied and practitioners have had to develop variational algorithms
on a case-by-case basis. In this paper, we develop two generic methods for
nonconjugate models, Laplace variational inference and delta method variational
inference. Our methods have several advantages: they allow for easily derived
variational algorithms with a wide class of nonconjugate models; they extend
and unify some of the existing algorithms that have been derived for specific
models; and they work well on real-world datasets. We studied our methods on
the correlated topic model, Bayesian logistic regression, and hierarchical
Bayesian logistic regression
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