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Nonparametric Regression Based on Hierarchical Interaction Models.
- Source :
-
IEEE Transactions on Information Theory . Mar2017, Vol. 63 Issue 3, p1620-1630. 11p. - Publication Year :
- 2017
-
Abstract
- In this paper, we introduce the so-called hierarchical interaction models, where we assume that the computation of the value of a function m: \mathbb R^d\rightarrow \mathbb R is done in several layers, where in each layer a function of at most d^* inputs computed by the previous layer is evaluated. We investigate two different regression estimates based on polynomial splines and on neural networks, and show that if the regression function satisfies a hierarchical interaction model and all occurring functions in the model are smooth, the rate of convergence of these estimates depends on d^* (and not on $d$ ). Hence, in this case, the estimates can achieve good rate of convergence even for large $d$ , and are in this sense able to circumvent the so-called curse of dimensionality. [ABSTRACT FROM PUBLISHER]
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 63
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 121340789
- Full Text :
- https://doi.org/10.1109/TIT.2016.2634401