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arXiv · 2601.01051

Quotient EM under Misspecification:Tight Local Rates and Finite-Sample Bounds in General Integral Probability Metrics

Koustav Mallik
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Abstract

We study the expectation-maximization (EM) algorithm for general latent-variable models under (i) distributional misspecification and (ii) nonidentifiability induced by a group action. We formulate EM on the quotient parameter space and measure error using an arbitrary integral probability metric (IPM). Our main results give (a) a sharp local linear convergence rate for population EM governed by the spectral radius of the linearization on a local slice, and (b) tight finite-sample bounds for sample EM obtained via perturbed contraction inequalities and generic chaining/entropy control of EM-induced empirical processes.

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Koustav Mallik. 2026-01-03. Quotient EM under Misspecification:Tight Local Rates and Finite-Sample Bounds in General Integral Probability Metrics. https://arxiv.org/abs/2601.01051

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