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- W4288091736 abstract "This paper investigates robust versions of the general empirical risk minimization algorithm, one of the core techniques underlying modern statistical methods. Success of the empirical risk minimization is based on the fact that for a well-behaved stochastic process $left{ f(X), fin mathcal Fright}$ indexed by a class of functions $fin mathcal F$, averages $frac{1}{N}sum_{j=1}^N f(X_j)$ evaluated over a sample $X_1,ldots,X_N$ of i.i.d. copies of $X$ provide good approximation to the expectations $mathbb E f(X)$ uniformly over large classes $fin mathcal F$. However, this might no longer be true if the marginal distributions of the process are heavy-tailed or if the sample contains outliers. We propose a version of empirical risk minimization based on the idea of replacing sample averages by robust proxies of the expectation, and obtain high-confidence bounds for the excess risk of resulting estimators. In particular, we show that the excess risk of robust estimators can converge to $0$ at fast rates with respect to the sample size. We discuss implications of the main results to the linear and logistic regression problems, and evaluate the numerical performance of proposed methods on simulated and real data." @default.
- W4288091736 created "2022-07-28" @default.
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- W4288091736 date "2019-10-16" @default.
- W4288091736 modified "2023-10-11" @default.
- W4288091736 title "Excess risk bounds in robust empirical risk minimization" @default.
- W4288091736 doi "https://doi.org/10.48550/arxiv.1910.07485" @default.
- W4288091736 hasPublicationYear "2019" @default.
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