Speaker: Meredith Kupinski, Optical Sciences, UA
Title: Robust Quadratic Observers for Detection
Date: Friday, April 11, 2025
Time: 4:00 pm
Place: Math building, Room 501
Abstract
When a single measurement is on the order of millions of elements, metrics which rely on statistical expectations over high-dimensional stochastic processes are nearly impossible to compute. Even when computational resources are limitless the quantity of sample data can be insufficient to form robust sample statistics required for mathematical observers. Estimating covariance/scatter matrices is a ubiquitous challenge without an obvious solution for high dimension, low sample size (HDLSS) problems. For HDLSS scenarios even simple operations, such as pre-whitening, are intractable because of the reliance on a full-rank covariance estimate. For higher quantities of training data machine learning can offer effective classification but does not provide insight about the informative correlation structure. Mathematical observers with capabilities to convert high-dimensional, heterogeneous data into information needed for hypothesis testing, data-driven discovery, and causal inferences are sought. This work considers heteroscedastic data from multiple sources which can be temporal, spatial, spectral, or a combine thereof. Covariance differences within one source of data or between different sources of data will be considered potentially informative. Linear transforms will be used to form robust estimates of HDLSS covariance. We will develop and demonstrate an inexact Manifold optimization algorithm to compute a linear transform that reduces dimensionality while preserving quadratic information. These robust quadratic observers are being developed to enable understandable non-linear post- processing that offers insight into capture system design based on data correlation structure.