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DTSTART;TZID=America/Los_Angeles:20221021T133000
DTEND;TZID=America/Los_Angeles:20221021T143000
DTSTAMP:20260425T134706
CREATED:20221018T155613Z
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SUMMARY:MLOpt: Lang Liu
DESCRIPTION:Speaker: Lang Liu\nTitle: Non-Asymptotic Analysis of M-Estimation for Statistical Learning and Inference under Self-Concordance \nAbstract: In this talk\, I discuss the problem of M-estimation for statistical learning and inference. It is well-known from the classical asymptotic theory that the properly centered and normalized estimator has a limiting Gaussian distribution with a sandwich covariance. I first establish a finite-sample bound for the estimator\, characterizing its asymptotic behavior in a non-asymptotic fashion. An important feature of the bound is that its dimension dependency is characterized by the effective dimension — the trace of the limiting sandwich covariance — which can be much smaller than the parameter dimension in some regimes. I then illustrate how the bound can be used to obtain a confidence set whose shape is adapted to the local curvature of the population risk. In contrast to previous work which relied heavily on the strong convexity of the learning objective\, I only assume the Hessian is lower bounded at optimum and allow it to gradually become degenerate. This property is formalized by the notion of self-concordance originating from convex optimization. Finally\, I apply these techniques to semi-parametric estimation and derive state-of-the-art finite-sample bounds for double machine learning and orthogonal statistical learning.
URL:https://ifds.info/event/mlopt-non-asymptotic-analysis-of-m-estimation-for-statistical-learning-and-inference-under-self-concordance/
LOCATION:University of Washington\, Seattle\, 185 E Stevens Way NE\, Seattle\, WA\, 98195-2350\, United States
CATEGORIES:MLOpt@UWash
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