Faculty Candidate EE Seminar - Boris Landa, Yale - Th. April 11, 4pm

Hosted by Rajit Manohar

Abstract:

Detecting and recovering a low-rank signal in a noisy data matrix is a key step in many data processing pipelines. A common approach for this task is to inspect and manipulate the spectrum of the observed data, typically by thresholding the singular values below a critical level. This approach is well-established for homoskedastic noise, where the variance is identical across the data entries. However, many real-world applications exhibit heteroskedastic noise whose characteristics vary considerably across the data, posing significant challenges for signal detection and recovery.

In this talk, I will present a principled approach for standardizing heteroskedastic noise by judiciously scaling the rows and columns of the data. This approach aims to enforce the standard spectral behavior of homoskedastic noise – the celebrated Marchenko-Pastur law, allowing for straightforward detection and recovery of signals. I will discuss two methods to determine the required scaling factors: one tailored for count data (e.g., Poisson, negative binomial) exhibiting a general variance pattern and another supporting general data types, albeit with a more restrictive variance pattern. I will demonstrate the effectiveness of these methods through simulations and real data, highlighting their benefits for signal detection and recovery in high dimensions and showcasing excellent agreement with the theory.

Bio: 

Boris Landa is an Associate Research Scientist in the Applied Mathematics Program at Yale University. His research focuses on developing theoretical and computational tools for processing and analyzing large experimental data. He is particularly interested in the challenges arising from heterogeneity, high dimensionality, noise, and deformations in data, commonly encountered in applications throughout science and engineering. Boris earned his BSc in Electrical Engineering from the Technion and a PhD in Applied Mathematics from Tel Aviv University. He joined the Mathematics Department at Yale in 2019 as a Gibbs Assistant Professor.