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By developing data augmentation methods unique to the negative binomial (NB) distribution, we unite seemingly disjoint count and mixture models under the NB process framework. We develop fundamental properties of the models and derive efficient Gibbs sampling inference. We show that the gamma-NB pro ...

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 ...

A dependent hierarchical beta process (dHBP) is developed as a prior for data that may be represented in terms of a sparse set of latent features, with covariate-dependent feature usage. The dHBP is applicable to general covariates and data models, imposing that signals with similar covariates ...