Name
Abstract | ||
|---|---|---|
We present formulas that allow us to decompose a function f of d variables into a sum of 2(d) terms f(u) indexed by subsets u of {1,..,d} where each term f(u) depends only on the variables with indices in u. The decomposition depends on the choice of d commuting projections {P-j}(j=1)(d) where P-j(f) does not depend on the variable x(j). We present an explicit formula for f(u), which is new even for the ANOVA and anchored decompositions; both are special cases of the general decomposition. We show that the decomposition is minimal in the following sense: if f is expressible as a sum in which there is no term that depends on all of the variables indexed by the subset z, then, for every choice of {P-j}(j=1)(d), the terms f(u) = 0 for all subsets u containing z. Furthermore, in a reproducing kernel Hilbert space setting, we give sufficient conditions for the terms f(u) to be mutually orthogonal. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1090/S0025-5718-09-02319-9 | MATHEMATICS OF COMPUTATION |
Keywords | Field | DocType |
indexation,reproducing kernel hilbert space | Hilbert space,Multivariate statistics,Mathematical analysis,Decomposition method (constraint satisfaction),Numerical analysis,Reproducing kernel Hilbert space,Mathematics | Journal |
Volume | Issue | ISSN |
79 | 270 | 0025-5718 |
Citations | PageRank | References |
18 | 1.33 | 11 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Frances Y. Kuo | 1 | 479 | 45.19 |
| Ian H. Sloan | 2 | 1180 | 183.02 |
| Grzegorz W. Wasilkowski | 3 | 527 | 167.51 |
| Henryk Wozniakowski | 4 | 130 | 28.31 |