Nonparametric Bayesian Dictionary Learning and Count and Mixture Modeling
Date
2013
Authors
Advisors
Journal Title
Journal ISSN
Volume Title
Repository Usage Stats
views
downloads
Abstract
Analyzing the ever-increasing data of unprecedented scale, dimensionality, diversity, and complexity poses considerable challenges to conventional approaches of statistical modeling. Bayesian nonparametrics constitute a promising research direction, in that such techniques can fit the data with a model that can grow with complexity to match the data. In this dissertation we consider nonparametric Bayesian modeling with completely random measures, a family of pure-jump stochastic processes with nonnegative increments. In particular, we study dictionary learning for sparse image representation using the beta process and the dependent hierarchical beta process, and we present the negative binomial process, a novel nonparametric Bayesian prior that unites the seemingly disjoint problems of count and mixture modeling. We show a wide variety of successful applications of our nonparametric Bayesian latent variable models to real problems in science and engineering, including count modeling, text analysis, image processing, compressive sensing, and computer vision.
Type
Department
Description
Provenance
Citation
Permalink
Citation
Zhou, Mingyuan (2013). Nonparametric Bayesian Dictionary Learning and Count and Mixture Modeling. Dissertation, Duke University. Retrieved from https://hdl.handle.net/10161/7204.
Collections
Except where otherwise noted, student scholarship that was shared on DukeSpace after 2009 is made available to the public under a Creative Commons Attribution / Non-commercial / No derivatives (CC-BY-NC-ND) license. All rights in student work shared on DukeSpace before 2009 remain with the author and/or their designee, whose permission may be required for reuse.