Publication Date
Summer 2026
Conference/Sponsorship/Institution
Twenty-Ninth Annual Conference on Artificial Intelligence and Statistics
Description
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 a fixed point algorithm for the MLE. Experiments show the fixed point 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 this algorithm leads to reproducibility for algorithms using MLE / CVE, and demonstrate how the algorithm leads to finding the MLE when the CV weights are known
Type
Article
Department
Mathematics
Link to published version
https://openreview.net/forum?id=OXTdMSkLxv
Recommended Citation
Kang, Keegan; Wang, Kerong; Zhang, Ding; Pratap, Rameshwar; Verma, Bhisham Dev; and Wong, Benedict, "It's All In The (Exponential) Family: An Equivalence Between Maximum Likelihood Estimation And Control Variates For Sketching Algorithms" (2026). Faculty Conference Papers and Presentations. 99.
https://digitalcommons.bucknell.edu/fac_conf/99