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

The distinction between local and global variables will be important for us to develop online inference. In Bayesian statistics, for example, think of β as parameters with a prior and z1:n as hidden variables which are individual to each observation. In a Bayesian mixture of Gaussians the global variables β are the mixture components and mixture… (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 compressive 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 a… (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)

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)

- Minhua Chen, Jorge G. Silva, John William Paisley, Chunping Wang, David B. Dunson, Lawrence Carin
- IEEE Transactions on Signal Processing
- 2010

Nonparametric Bayesian methods are employed to constitute a mixture of low-rank Gaussians, for data x ∈ R<sup>N</sup> that are of high dimension <i>N</i> but are constrained to reside in a low-dimensional subregion of R<sup>N</sup>. The number of mixture components and their rank are inferred automatically from the data. The resulting algorithm can… (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)

- Tamara Broderick, Lester W. Mackey, John William Paisley, Michael I. Jordan
- IEEE Transactions on Pattern Analysis and Machine…
- 2015

We develop a Bayesian nonparametric approach to a general family of latent class problems in which individuals can belong simultaneously to multiple classes and where each class can be exhibited multiple times by an individual. We introduce a combinatorial stochastic process known as the <italic>negative binomial process</italic> (<inline-formula>… (More)