Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: ERM and RERM are optimal estimators for regression problems when
  malicious outliers corrupt the labels   We study Empirical Risk Minimizers (ERM) and Regularized Empirical Risk
Minimizers (RERM) for regression problems with convex and $L$-Lipschitz loss
functions. We consider a setting where $|\cO|$ malicious outliers contaminate
the labels. In that case, under a local Bernstein condition, we show that the
$L_2$-error rate is bounded by $ r_N + AL |\cO|/N$, where $N$ is the total
number of observations, $r_N$ is the $L_2$-error rate in the non-contaminated
setting and $A$ is a parameter coming from the local Bernstein condition. When
$r_N$ is minimax-rate-optimal in a non-contaminated setting, the rate $r_N +
AL|\cO|/N$ is also minimax-rate-optimal when $|\cO|$ outliers contaminate the
label. The main results of the paper can be used for many non-regularized and
regularized procedures under weak assumptions on the noise. We present results
for Huber's M-estimators (without penalization or regularized by the
$\ell_1$-norm) and for general regularized learning problems in reproducible
kernel Hilbert spaces when the noise can be heavy-tailed.

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The categories of this paper are: hep-th
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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat
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The categories of this paper are: bayes-an
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The categories of this paper are: physics
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The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: econ
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The categories of this paper are: nlin