Carsten Peterson
Determining dependency structures and estimating nonlinear regression errors without doing regression
Proceedings of the Fourth International Workshop on Software Engineering and Artificial Intelligence for High Energy and Nuclear Physics, eds. B. Denby and D. Perret-Gallix, International Journal of Modern Physics 6, 611-616 (1995)

A general method is discussed, the δ-test, which establishes functional dependencies given a table of measurements. The approach is based on calculating conditional probabilities from data densities. Imposing the requirement of continuity of the underlying function the obtained values of the conditional probabilities carry information on the variable dependencies. The power of the method is illustrated on synthetic time-series with different time-lag dependencies and noise levels. For N data points the computational demand is N2. Also, the same method is used for estimating nonlinear regression errors and their distributions without performing regression. Comparing the predicted residual errors with those from linear models provides a signal for nonlinearity. The virtue of the method in the context of feedforward neural networks is stressed with respect to preprocessing data and tracking residual errors.

LU TP 95-04