In exponential families where the target parameters equal the mean parameters, optimal control variate estimators and maximum likelihood estimators have identical asymptotic variance, giving a fixed-point algorithm for the MLE.
EM algorithm and variants: an informal tutorial
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The expectation-maximization (EM) algorithm introduced by Dempster et al in 1977 is a very general method to solve maximum likelihood estimation problems. In this informal report, we review the theory behind EM as well as a number of EM variants, suggesting that beyond the current state of the art is an even much wider territory still to be discovered.
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It's all In the (Exponential) Family: An Equivalence between Maximum Likelihood Estimation and Control Variates for Sketching Algorithms
In exponential families where the target parameters equal the mean parameters, optimal control variate estimators and maximum likelihood estimators have identical asymptotic variance, giving a fixed-point algorithm for the MLE.