STOR Colloquium: Anna Little, Michigan State University

Robust Statistical Procedures for Noisy,

High-dimensional Data

This talk addresses two topics related to robust statistical procedures for analyzing noisy, high-dimensional data: (I) path-based spectral clustering and (II) robust multi-reference alignment. Both methods must overcome a large ambient dimension and lots of noise to extract the relevant low dimensional data structure in a computationally efficient way. In (I), the goal is to partition the data into meaningful groups, and this is achieved by a novel approach which combines a data driven metric with graph-based clustering. Using a data driven metric allows for strong theoretical guarantees and fast algorithms when clusters concentrate around low-dimensional sets. In (II), the goal is to recover a hidden signal from many noisy observations of the hidden signal, where each noisy observation includes a random translation, a random dilation, and high additive noise. A wavelet based approach is used to apply a data-driven, nonlinear unbiasing procedure, so that the estimate of the hidden signal is robust to high frequency perturbations.

Refreshments will be served at 3:00pm in the 3^rd floor lounge of Hanes Hall