The II Method for Estimating Multivariate Functions From Noisy Data
- 1 May 1991
- journal article
- research article
- Published by Taylor & Francis Ltd in Technometrics
- Vol. 33 (2), 125-143
- https://doi.org/10.1080/00401706.1991.10484799
Abstract
The Π method for estimating an underlying smooth function of M variables, (x l , …, xm ), using noisy data is based on approximating it by a sum of products of the form Π m φ m (x m ). The problem is then reduced to estimating the univariate functions in the products. A convergent algorithm is described. The method keeps tight control on the degrees of freedom used in the fit. Many examples are given. The quality of fit given by the Π method is excellent. Usually, only a few products are enough to fit even fairly complicated functions. The coding into products of univariate functions allows a relatively understandable interpretation of the multivariate fit.Keywords
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