Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Performance of empirical risk minimization in linear aggregation   We study conditions under which, given a dictionary $F=\{f_1,\ldots ,f_M\}$
and an i.i.d. sample $(X_i,Y_i)_{i=1}^N$, the empirical minimizer in
$\operatorname {span}(F)$ relative to the squared loss, satisfies that with
high probability
\[R\bigl(\tilde{f}^{\mathrm{ERM}}\bigr)\leq\inf_{f\in\operatorname
{span}(F)}R(f)+r_N(M),\] where $R(\cdot)$ is the squared risk and $r_N(M)$ is
of the order of $M/N$. Among other results, we prove that a uniform small-ball
estimate for functions in $\operatorname {span}(F)$ is enough to achieve that
goal when the noise is independent of the design.

1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: math-ph
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph