Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 570509, 15 pages
Research Article

An Algorithm for Optimally Fitting a Wiener Model

1Intel Corporation, Hillsboro, OR 97124, USA
2Department of Statistics, Iowa State University, Ames, IA 50010, USA
3Department of Chemical & Biological Engineering, Iowa State University, Ames, IA 50010, USA
4BodyMedia Inc., 420 Fort Duquesne Boulevard, Pittsburgh, PA 15222, USA

Received 2 September 2010; Accepted 15 September 2011

Academic Editor: Elbert Macau

Copyright © 2011 Lucas P. Beverlin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The purpose of this work is to present a new methodology for fitting Wiener networks to datasets with a large number of variables. Wiener networks have the ability to model a wide range of data types, and their structures can yield parameters with phenomenological meaning. There are several challenges to fitting such a model: model stiffness, the nonlinear nature of a Wiener network, possible overfitting, and the large number of parameters inherent with large input sets. This work describes a methodology to overcome these challenges by using several iterative algorithms under supervised learning and fitting subsets of the parameters at a time. This methodology is applied to Wiener networks that are used to predict blood glucose concentrations. The predictions of validation sets from models fit to four subjects using this methodology yielded a higher correlation between observed and predicted observations than other algorithms, including the Gauss-Newton and Levenberg-Marquardt algorithms.