Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Higher order Sobol' indices   Sobol' indices measure the dependence of a high dimensional function on
groups of variables defined on the unit cube $[0,1]^d$. They are based on the
ANOVA decomposition of functions, which is an $L^2$ decomposition. In this
paper we discuss generalizations of Sobol' indices which yield $L^p$ measures
of the dependence of $f$ on subsets of variables. Our interest is in values
$p>2$ because then variable importance becomes more about reaching the extremes
of $f$. We introduce two methods. One based on higher order moments of the
ANOVA terms and another based on higher order norms of a spectral decomposition
of $f$, including Fourier and Haar variants. Both of our generalizations have
representations as integrals over $[0,1]^{kd}$ for $k\ge 1$, allowing direct
Monte Carlo or quasi-Monte Carlo estimation. We find that they are sensitive to
different aspects of $f$, and thus quantify different notions of variable
importance.

34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org