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Bayes High-Dimensional Density Estimation Using Multiscale Dictionaries

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Date
2014
Author
Wang, Ye
Advisor
Dunson, David B
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Abstract

Although Bayesian density estimation using discrete mixtures has good performance in modest dimensions, there is a lack of statistical and computational scalability to high-dimensional multivariate cases. To combat the curse of dimensionality, it is necessary to assume the data are concentrated near a lower-dimensional subspace. However, Bayesian methods for learning this subspace along with the density of the data scale poorly computationally. To solve this problem, we propose an empirical Bayes approach, which estimates a multiscale dictionary using geometric multiresolution analysis in a first stage. We use this dictionary within a multiscale mixture model, which allows uncertainty in component allocation, mixture weights and scaling factors over a binary tree. A computational algorithm is proposed, which scales efficiently to massive dimensional problems. We provide some theoretical support for this method, and illustrate the performance through simulated and real data examples.

Type
Master's thesis
Department
Statistical and Economic Modeling
Subject
Statistics
dictionary learning
empirical Bayes
geometric multiresolution analysis
nonparametric Bayes
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https://hdl.handle.net/10161/8840
Citation
Wang, Ye (2014). Bayes High-Dimensional Density Estimation Using Multiscale Dictionaries. Master's thesis, Duke University. Retrieved from https://hdl.handle.net/10161/8840.
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