SILO



The weekly SILO Seminar Series is made possible through the generous support of the 3M Company and its Advanced Technology Group

3M

with additional support from the Analytics Group of the Northwestern Mutual Life Insurance Company

Northwestern Mutual

Universality laws for randomized dimension reduction

Joel Tropp, Professor, Applied & Computational Mathematics, California Institute of Technology

Date and Time: Apr 13, 2016 (12:30 PM)
Location: Orchard room (3280) at the Wisconsin Institute for Discovery Building

Abstract:

Video: https://vimeo.com/162964879

Dimension reduction is the process of embedding high-dimensional data into a lower dimensional space to facilitate its analysis. In the Euclidean setting, one fundamental technique for dimension reduction is to apply a random linear map to the data. The question is how large the embedding dimension must be to ensure that randomized dimension reduction succeeds with high probability.

This talk describes a phase transition in the behavior of the dimension reduction map as the embedding dimension increases. The location of this phase transition is universal for a large class of datasets and random dimension reduction maps. Furthermore, the stability properties of randomized dimension reduction are also universal. These results have many applications in numerical analysis, signal processing, and statistics.

Joint work with Samet Oymak.