Women in Mathematics Talks

Compressed Anomaly Detection with Multiple Mixed Observations

Natalie Durgin

Natalie Durgin ’09 is a Research Staff Member at the Center for Communications Research in La Jolla, CA. Previously she worked as a Senior Data Scientist at Spiceworks, an Austin tech company. During her four-year tenure, she built a diverse set of statistical and machine learning models for prediction, classification, optimization, and natural language processing. She earned a Ph.D. in mathematics at Rice University, where she studied Algebraic Geometry and Geometric Invariant Theory. After hours, she enjoys rock climbing, cooking, and solving the “Monday Punday”.

Abstract

Nowadays, data is pouring in from all directions. Whether it emanates from financial markets or agricultural soil sensors, we can think of each data feature as a random variable with a probability distribution. Suppose we have an enormous collection of independent random variables that are identically distributed except for a few anomalies. How can we efficiently detect these anomalies without copiously sampling each of the random variables and conducting individual hypothesis tests? Recent work* proposes to ease the pain by conducting hypothesis tests based on mixed observations (e.g. linear combinations) of the random variables. In this talk, we will relate this mixed observation scenario to the compressed sensing concept of multiple measurement vectors (MMVs). Many algorithms have been developed for recovering jointly sparse signals and their support from MMVs. We will establish the theoretical and empirical effectiveness of some of these existing algorithms at detecting anomalous random variables.

Friday, October 29, 2021, at 4 p.m. (PT) in HMC‘s Shanahan Center 1430