MULTIVARIATE REGRESSION AND MACHINE LEARNING WITH SUMS OF SEPARABLE FUNCTIONS

被引：72

作者：

Beylkin, Gregory ^{[1
]}

Garcke, Jochen ^{[2
]}

Mohlenkamp, Martin J. ^{[3
]}

机构：

[1] Univ Colorado, Dept Appl Math, Boulder, CO 80309 USA

[2] Tech Univ Berlin, Inst Math, D-10623 Berlin, Germany

[3] Ohio Univ, Dept Math, Athens, OH 45701 USA

来源：

SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2009年 / 31卷 / 03期

关键词：

multivariate regression; machine learning; curse of dimensionality; separation of variables; SPARSE GRIDS; APPROXIMATION; ALGORITHMS; DIMENSIONS;

D O I：

10.1137/070710524

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present an algorithm for learning (or estimating) a function of many variables from scattered data. The function is approximated by a sum of separable functions, following the paradigm of separated representations. The central fitting algorithm is linear in both the number of data points and the number of variables and, thus, is suitable for large data sets in high dimensions. We present numerical evidence for the utility of these representations. In particular, we show that our method outperforms other methods on several benchmark data sets.

引用

页码：1840 / 1857

页数：18

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