Roughness/error trade-offs in neural network time series models

Steven C. Gustafson; Gordon R. Little; John S. Loomis; Theresa A. Tuthill

doi:10.1117/12.271469

4 April 1997 Roughness/error trade-offs in neural network time series models

Steven C. Gustafson, Gordon R. Little, John S. Loomis, Theresa A. Tuthill

Proceedings Volume 3077, Applications and Science of Artificial Neural Networks III; (1997) https://doi.org/10.1117/12.271469
Event: AeroSense '97, 1997, Orlando, FL, United States

Abstract

Radial basis function neural network models of a time series may be developed or trained using samples from the series. Each model is a continuous curve that can be used to represent the series or predict future vales. Model development requires a tradeoff between a measure of roughness of the curve and a measure of its error relative to the samples. For roughness defined as the root integrated squared second derivative and for error defined as the root sum squared deviation (which are among the most common definitions), an optimal tradeoff conjecture is proposed and illustrated. The conjecture states that the curve that minimizes roughness subject to given error is a weighted mean of the least squares line and the natural cubic spline through the samples.

Citation Download Citation

Steven C. Gustafson, Gordon R. Little, John S. Loomis, and Theresa A. Tuthill "Roughness/error trade-offs in neural network time series models", Proc. SPIE 3077, Applications and Science of Artificial Neural Networks III, (4 April 1997); https://doi.org/10.1117/12.271469

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