*********************************
There is now a CONTENT FREEZE for Mercury while we switch to a new platform. It began on Friday, March 10 at 6pm and will end on Wednesday, March 15 at noon. No new content can be created during this time, but all material in the system as of the beginning of the freeze will be migrated to the new platform, including users and groups. Functionally the new site is identical to the old one. webteam@gatech.edu
*********************************
Title: Finding and Exploiting Intrinsic Low Dimension in High-dimensional Inference
Committee:
Dr. Davenport, Advisor
Dr. Romberg, Chair
Dr. Koltchinskii
Abstract:
The objective of the proposed research is to develop and analyze algorithms for high-dimensional statistical inference and machine learning that exploit intrinsic low-dimensional structure. We want to show that the sample complexity and susceptibility to noise of such algorithms is determined by the relatively low intrinsic dimension rather than the high ambient dimension. In addition to our prior low-rank matrix completion and denoising work, we specifically consider the application of reproducing kernel Hilbert space methods to function estimation on a manifold. We want to show that the complexity of estimating functions on a manifold scales with the manifold dimension; we furthermore want to show that, for manifolds embedded in high-dimensional space, this can be achieved with practical, manifold-agnostic kernel methods.
