| Abstract: |
The main theme of this thesis is to develop computational methods and
their corresponding statistical foundations to conduct effective
nonparametric inference in high dimensions. The result will be a
rigorous theoretical framework and the corresponding learning algorithms
that exploit hidden structure to overcome the curse of dimensionality
when analyzing high-dimensional datasets.
In this talk, I will inroduce some recent methods that can avoid the curse using different regularization mechanisms, including RODEO (Regularization of Derivative Expectation Operator), COSSO (Component Selection and Smoothing Operator), and SpAM (Sparse Additive Mdoels). All of them can be viewed as functional versions of the popular LASSO (Least Absolute Shrinkage and Selection Operator) estimator in the linear model literature. I will also describe some extensions of these ideas in new directions, including sparse high-dimensional density estimation using the rodeo, multi-task sparse additive models, and nonparametric graphical model learning. The remaining tasks and problems I am going to solve will also be presented. Thesis Committee: Co-chairs; John Lafferty & Larry Wasserman, Christopher Genovese, Zoubin Ghahramani, Bin Yu (U.C. Berkeley). http://www.cs.cmu.edu/~hanliu/prop/Proposal.pdf
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