These lecture notes synthesize robust statistical learning theory, showing how median-of-means, minimax, homogeneity, and small-ball principles yield oracle inequalities for both ERM and robust estimators.
Distributed Statistical Estimation and Rates of Convergence in Normal Approximation
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abstract
This paper presents a class of new algorithms for distributed statistical estimation that exploit divide-and-conquer approach. We show that one of the key benefits of the divide-and-conquer strategy is robustness, an important characteristic for large distributed systems. We establish connections between performance of these distributed algorithms and the rates of convergence in normal approximation, and prove non-asymptotic deviations guarantees, as well as limit theorems, for the resulting estimators. Our techniques are illustrated through several examples: in particular, we obtain new results for the median-of-means estimator, as well as provide performance guarantees for distributed maximum likelihood estimation.
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2019 1verdicts
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Lecture Notes: Selected topics on robust statistical learning theory
These lecture notes synthesize robust statistical learning theory, showing how median-of-means, minimax, homogeneity, and small-ball principles yield oracle inequalities for both ERM and robust estimators.