Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Measuring the interactions among variables of functions over the unit
  hypercube   By considering a least squares approximation of a given square integrable
function $f\colon[0,1]^n\to\R$ by a multilinear polynomial of a specified
degree, we define an index which measures the overall interaction among
variables of $f$. This definition extends the concept of Banzhaf interaction
index introduced in cooperative game theory. Our approach is partly inspired
from multilinear regression analysis, where interactions among the independent
variables are taken into consideration. We show that this interaction index has
appealing properties which naturally generalize the properties of the Banzhaf
interaction index. In particular, we interpret this index as an expected value
of the difference quotients of $f$ or, under certain natural conditions on $f$,
as an expected value of the derivatives of $f$. These interpretations show a
strong analogy between the introduced interaction index and the overall
importance index defined by Grabisch and Labreuche [7]. Finally, we discuss a
few applications of the interaction index.

14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci