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- Matthew D. Hoffman, David M. Blei, Chong Wang, John William Paisley
- Journal of Machine Learning Research
- 2013

We derive a stochastic optimization algorithm for mean field variational inference, which we call online variational inference. Our algorithm approximates the posterior distribution of a probabilistic model with hidden variables, and can handle large (or even streaming) data sets of observations. Let x = x 1:n be n observations, β be global hidden… (More)

- Mingyuan Zhou, Haojun Chen, +6 authors Lawrence Carin
- IEEE Transactions on Image Processing
- 2012

Nonparametric Bayesian methods are considered for recovery of imagery based upon compressive, incomplete, and/or noisy measurements. A truncated beta-Bernoulli process is employed to infer an appropriate dictionary for the data under test and also for image recovery. In the context of compressive sensing, significant improvements in image recovery are… (More)

- John William Paisley, Lawrence Carin
- ICML
- 2009

We propose a nonparametric extension to the factor analysis problem using a beta process prior. This <i>beta process factor analysis</i> (BP-FA) model allows for a dataset to be decomposed into a linear combination of a sparse set of factors, providing information on the underlying structure of the observations. As with the Dirichlet process, the beta… (More)

- Chong Wang, John William Paisley, David M. Blei
- AISTATS
- 2011

The hierarchical Dirichlet process (HDP) is a Bayesian nonparametric model that can be used to model mixed-membership data with a potentially infinite number of components. It has been applied widely in probabilistic topic modeling, where the data are documents and the components are distributions of terms that reflect recurring patterns (or " topics ") in… (More)

Non-parametric Bayesian techniques are considered for learning dictionaries for sparse image representations, with applications in denoising, inpainting and com-pressive sensing (CS). The beta process is employed as a prior for learning the dictionary, and this non-parametric method naturally infers an appropriate dictionary size. The Dirichlet process and… (More)

- John William Paisley, Lawrence Carin
- IEEE Transactions on Signal Processing
- 2009

The number of states in a hidden Markov model (HMM) is an important parameter that has a critical impact on the inferred model. Bayesian approaches to addressing this issue include the nonparametric hierarchical Dirichlet process, which does not extend to a variational Bayesian (VB) solution. We present a fully conjugate, Bayesian approach to determining… (More)

We present the discrete infinite logistic normal distribution (DILN), a Bayesian nonparametric prior for mixed membership models. DILN generalizes the hierarchical Dirichlet process (HDP) to model correlation structure between the weights of the atoms at the group level. We derive a representation of DILN as a normalized collection of gamma-distributed… (More)

- John William Paisley, Chong Wang, David M. Blei
- AISTATS
- 2011

We present the discrete infinite logistic normal distribution (DILN, " Dylan "), a Bayesian non-parametric prior for mixed membership models. DILN is a generalization of the hierarchical Dirichlet process (HDP) that models correlation structure between the weights of the atoms at the group level. We derive a representation of DILN as a normalized collection… (More)

Mean-field variational inference is a method for approximate Bayesian posterior inference. It approximates a full posterior distribution with a factorized set of distributions by maximizing a lower bound on the marginal likelihood. This requires the ability to integrate a sum of terms in the log joint likelihood using this factorized distribution. Often not… (More)

- John William Paisley, Chong Wang, David M. Blei, Michael I. Jordan
- IEEE Transactions on Pattern Analysis and Machine…
- 2015

We develop a nested hierarchical Dirichlet process (nHDP) for hierarchical topic modeling. The nHDP generalizes the nested Chinese restaurant process (nCRP) to allow each word to follow its own path to a topic node according to a per-document distribution over the paths on a shared tree. This alleviates the rigid, single-path formulation assumed by the… (More)