12:30–1:30 pm
Tuesday, April 30, 2024, at 12:30 PM, in Searle 240A, 5735 S. Ellis Avenue
CAM & Stats Student Seminar
Phillip Lo, Committee on Computational and Applied Mathematics
"The Sample Complexity of Noisy Curve Recovery"
Abstract
We consider the problem of recovering a high dimensional curve from noisy observations. In the low noise regime, a straightforward approach of locally approximating the data with curves is feasible. However, in the high noise regime, it becomes impossible to localize any data point to a portion of the curve. Indeed, we will demonstrate an information-theoretic lower bound on the sample complexity of high-noise curve recovery, that the number of observations needed to estimate a curve with high noise is cubic in the noise level. We will then show preliminary results on a third-moment based recovery algorithm for recovering noisy curves with a particular multiscale structure. Joint work with Yuehaw Khoo.