It’s all in the Exponential Family: An Equivalence Between Maximum Likelihood Estimation and Control Variates for Sketching Algorithms
As part of the Bucknell Physics and Astronomy summer research program, the work of Keegan Kang (Assistant Professor of Statistics), Kerong Wang ’24, and their collaborators was accepted to AISTATS 2026. The Bucknell Physics and Astronomy summer research program is an annual program for student researchers working with faculty members in Physics and Astronomy, as well as students from Mathematics and Statistics by invitation.
This project was first proposed by Devon Zhang ’23 to investigate the performance of estimators in sketching algorithms, and was accepted at a lightning session in SDSS 2023. It was developed into a full research project on the properties of these estimators by Kerong Wang ’24, who participated in the Bucknell Physics and Astronomy summer research program, mentored by Keegan Kang. This project then garnered interest with international collaborators Rameshwar Pratap, Bhisham Dev Verma, and Benedict H.W. Wong, who contributed to extensive simulations, and culminated in the acceptance of this paper to AISTATS 2026.
The paper ties together two fundamental estimators: a) maximum likelihood estimation, taught in Bucknell’s statistical inference classes such as STAT 304 (Statistical Inference Theory), and b) control variates, taught in Bucknell’s computational statistics classes such as STAT 354 (Modern Data Analysis). Under some conditions, these two estimators have the same asymptotic variance where maximizing the likelihood gives the same result as minimizing the variance. This gives rise to an efficient algorithm to compute the maximum likelihood estimator with improved speed and numerical stability.
