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 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.
From: Keegan Kang [view email]
[v1]
Thu, 29 Jan 2026 22:41:43 UTC (1,387 KB)
[v2]
Wed, 4 Feb 2026 17:35:28 UTC (1,387 KB)
[v3]
Sat, 4 Jul 2026 21:34:49 UTC (1,404 KB)
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