Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An invariance property of kernel based predictors   We consider kernel based learning methods for regression and analyze what
happens to the risk minimizer when new variables, statistically independent of
input and target variables, are added to the set of input variables; this
problem arises, for example, in the detection of causality relations between
two time series. We find that the risk minimizer remains unchanged if we
constrain the risk minimization to hypothesis spaces induced by suitable kernel
functions. We show that not all kernel induced hypothesis spaces enjoy this
property. We present sufficient conditions ensuring that the risk minimizer
does not change, and show that they hold for inhomogeneous polynomial and
Gaussian RBF kernels. We also provide examples of kernel induced hypothesis
spaces whose risk minimizer changes if independent variables are added as
input.

25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
2
The categories of this paper are: math
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph