Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Concentration inequalities of the cross-validation estimator for
  Empirical Risk Minimiser   In this article, we derive concentration inequalities for the
cross-validation estimate of the generalization error for empirical risk
minimizers. In the general setting, we prove sanity-check bounds in the spirit
of \cite{KR99} \textquotedblleft\textit{bounds showing that the worst-case
error of this estimate is not much worse that of training error estimate}
\textquotedblright . General loss functions and class of predictors with finite
VC-dimension are considered. We closely follow the formalism introduced by
\cite{DUD03} to cover a large variety of cross-validation procedures including
leave-one-out cross-validation, $k$% -fold cross-validation, hold-out
cross-validation (or split sample), and the leave-$\upsilon$-out
cross-validation.
  In particular, we focus on proving the consistency of the various
cross-validation procedures. We point out the interest of each cross-validation
procedure in terms of rate of convergence. An estimation curve with transition
phases depending on the cross-validation procedure and not only on the
percentage of observations in the test sample gives a simple rule on how to
choose the cross-validation. An interesting consequence is that the size of the
test sample is not required to grow to infinity for the consistency of the
cross-validation procedure.

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The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: econ
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
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The categories of this paper are: q-alg
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The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con