Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The theory and application of penalized methods or Reproducing Kernel
  Hilbert Spaces made easy   The popular cubic smoothing spline estimate of a regression function arises
as the minimizer of the penalized sum of squares $\sum_j(Y_j - {\mu}(t_j))^2 +
{\lambda}\int_a^b [{\mu}"(t)]^2 dt$, where the data are $t_j,Y_j$, $j=1,...,
n$. The minimization is taken over an infinite-dimensional function space, the
space of all functions with square integrable second derivatives. But the
calculations can be carried out in a finite-dimensional space. The reduction
from minimizing over an infinite dimensional space to minimizing over a finite
dimensional space occurs for more general objective functions: the data may be
related to the function ${\mu}$ in another way, the sum of squares may be
replaced by a more suitable expression, or the penalty, $\int_a^b [{\mu}"(t)]^2
dt$, might take a different form. This paper reviews the Reproducing Kernel
Hilbert Space structure that provides a finite-dimensional solution for a
general minimization problem. Particular attention is paid to penalties based
on linear differential operators. In this case, one can sometimes easily
calculate the minimizer explicitly, using Green's functions.

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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: econ
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
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The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph
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The categories of this paper are: math-ph
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The categories of this paper are: comp-gas