Quotient EM under Misspecification:Tight Local Rates and Finite-Sample Bounds in General Integral Probability Metrics
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911352376786944 |
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| author | Mallik, Koustav |
| author_facet | Mallik, Koustav |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_01051 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quotient EM under Misspecification:Tight Local Rates and Finite-Sample Bounds in General Integral Probability Metrics Mallik, Koustav Statistics Theory Methodology 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. |
| title | Quotient EM under Misspecification:Tight Local Rates and Finite-Sample Bounds in General Integral Probability Metrics |
| topic | Statistics Theory Methodology |
| url | https://arxiv.org/abs/2601.01051 |