I Rivals | PubMed Health

PubMed1999

On cross validation for model selection.

In response to Zhu and Rower (1996), a recent communication (Goutte, 1997) established that leave-one-out cross validation is not subject to the "no-free-lunch" criticism. Despite this optimistic conclusion, we show here that cross validation has very poor performances for the selection of linear models as compared to classic statistical tests. We conclude that the statistical tests are preferable to cross validation for linear as well as for nonlinear model selection.

Linear Models↗

PubMedDate not supplied

Construction of confidence intervals for neural networks based on least squares estimation.

We present the theoretical results about the construction of confidence intervals for a nonlinear regression based on least squares estimation and using the linear Taylor expansion of the nonlinear model output. We stress the assumptions on which these results are based, in order to derive an appropriate methodology for neural black-box modeling; the latter is then analyzed and illustrated on simulated and real processes. We show that the linear Taylor expansion of a nonlinear model output also gives a tool to detect the possible ill-conditioning of neural network candidates, and to estimate their performance. Finally, we show that the least squares and linear Taylor expansion based approach compares favorably with other analytic approaches, and that it is an efficient and economic alternative to the nonanalytic and computationally intensive bootstrap methods.

Confidence Intervals↗