{"ID":2823009,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2601.01051","arxiv_id":"2601.01051","title":"Quotient EM under Misspecification:Tight Local Rates and Finite-Sample Bounds in General Integral Probability Metrics","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.","short_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 result...","url_abs":"https://arxiv.org/abs/2601.01051","url_pdf":"https://arxiv.org/pdf/2601.01051v1","authors":"[\"Koustav Mallik\"]","published":"2026-01-03T03:09:10Z","proceeding":"math.ST","tasks":"[\"math.ST\",\"stat.ME\"]","methods":"[]","has_code":false}