Bayesian and Information-Theoretic Learning of High Dimensional Data

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Date

2012

Authors

Chen, Minhua

Advisors

Carin, Lawrence

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Abstract

The concept of sparseness is harnessed to learn a low dimensional representation of high dimensional data. This sparseness assumption is exploited in multiple ways. In the Bayesian Elastic Net, a small number of correlated features are identified for the response variable. In the sparse Factor Analysis for biomarker trajectories, the high dimensional gene expression data is reduced to a small number of latent factors, each with a prototypical dynamic trajectory. In the Bayesian Graphical LASSO, the inverse covariance matrix of the data distribution is assumed to be sparse, inducing a sparsely connected Gaussian graph. In the nonparametric Mixture of Factor Analyzers, the covariance matrices in the Gaussian Mixture Model are forced to be low-rank, which is closely related to the concept of block sparsity.

Finally in the information-theoretic projection design, a linear projection matrix is explicitly sought for information-preserving dimensionality reduction. All the methods mentioned above prove to be effective in learning both simulated and real high dimensional datasets.

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Subjects

Electrical engineering, Statistics, Computer science, Bayesian Statistics, High Dimensional Data Analysis, Information-Theoretic Learning, Machine Learning, Signal Processing, Sparseness

Citation

Citation

Chen, Minhua (2012). Bayesian and Information-Theoretic Learning of High Dimensional Data. Dissertation, Duke University. Retrieved from https://hdl.handle.net/10161/5588.

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Dukes student scholarship is made available to the public using a Creative Commons Attribution / Non-commercial / No derivative (CC-BY-NC-ND) license.