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dc.contributor.advisor Carin, Lawrence en_US
dc.contributor.author Paisley, John William en_US
dc.date.accessioned 2010-05-10T20:17:36Z
dc.date.available 2010-05-10T20:17:36Z
dc.date.issued 2010 en_US
dc.identifier.uri http://hdl.handle.net/10161/2458
dc.description Dissertation en_US
dc.description.abstract <p>Bayesian nonparametric methods are useful for modeling data without having to define the complexity of the entire model <italic>a priori</italic>, but rather allowing for this complexity to be determined by the data. Two problems considered in this dissertation are the number of components in a mixture model, and the number of factors in a latent factor model, for which the Dirichlet process and the beta process are the two respective Bayesian nonparametric priors selected for handling these issues.</p> <p>The flexibility of Bayesian nonparametric priors arises from the prior's definition over an infinite dimensional parameter space. Therefore, there are theoretically an <italic>infinite</italic> number of latent components and an <italic>infinite</italic> number of latent factors. Nevertheless, draws from each respective prior will produce only a small number of components or factors that appear in a given data set. As mentioned, the number of these components and factors, and their corresponding parameter values, are left for the data to decide.</p> <p>This dissertation is split between novel practical applications and novel theoretical results for these priors. For the Dirichlet process, we investigate stick-breaking representations for the finite Dirichlet process and their application to novel sampling techniques, as well as a novel mixture modeling framework that incorporates multiple modalities within a data set. For the beta process, we present a new stick-breaking construction for the infinite-dimensional prior, and consider applications to image interpolation problems and dictionary learning for compressive sensing.</p> en_US
dc.format.extent 14589534 bytes
dc.format.mimetype application/pdf
dc.language.iso en_US
dc.subject Engineering, Electronics and Electrical en_US
dc.subject Statistics en_US
dc.subject beta process en_US
dc.subject Dirichlet process en_US
dc.subject factor models en_US
dc.subject machine learning en_US
dc.subject mixture models en_US
dc.title Machine Learning with Dirichlet and Beta Process Priors: Theory and Applications en_US
dc.type Dissertation en_US
dc.department Electrical and Computer Engineering en_US

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