It’s All In The (Exponential) Family: An Equivalence Between Maximum Likelihood Estimation and Control Variates For Sketching Algorithms

Title of the Talk: It’s All In The (Exponential) Family: An Equivalence Between Maximum Likelihood Estimation and Control Variates For Sketching Algorithms
Speakers: Dr. Keegan Kang
Host Faculty: Dr.Rameshwar Pratap
Date: Dec 22, 2025
Time: 12:00 pm.
Venue: CSE-LH2

Abstract: Maximum likelihood estimators (MLE) and control variate estimators (CVE) have been used in conjunction with known information across sketching algorithms and applications in machine learning. We prove that under certain conditions in an exponential family, an optimal CVE will achieve the same asymptotic variance as the MLE, giving an Expectation-Maximization (EM) algorithm for the MLE. Experiments show the EM algorithm is faster and numerically stable compared to other root-finding algorithms for the MLE for the bivariate Normal distribution, and we expect this to hold across distributions satisfying these conditions. We show how the EM algorithm leads to reproducibility for algorithms using MLE / CVE, and demonstrate how the EM algorithm leads to finding the MLE when the CV weights are known

Bio: Keegan Kang is an assistant professor of statistics at Bucknell University, USA. He earned a PhD in statistics from Cornell University. His research interests are in mathematical statistics, hashing algorithms, and differential privacy