ASMOD (Adaptive Spline Modelling of Observation Data): some theoretical and experimental results

The ASMOD algorithm uses B-splines for identifying and representing nonlinear dependencies in multidimensional observation data. By automatically adjusting the internal structure of the model to the dependencies identified in the data, the model can be made flexible enough to model general and coupled nonlinear dependencies. At the same time the flexibility of the model with respect to other not yet identified dependencies is restricted, thus avoiding overfitting to random fluctuations in the data. The algorithm has been applied to several real and synthetic data sets, and good performance has been demonstrated. The model is fitted to a data set by minimisation of the mean square error of the estimate for the target variable. Online iterative or offline matrix based methods may be used for optimisation. Theoretical work based on the Vapnik-Chervonenkis dimension and the risk minimisation principle has shown that upper and lower bounds can be found for the expected mean squared error provided some weak assumptions about the data are satisfied. These bounds depend on the number of parameters in the model and the number of observations. Convergence to an optimal solution when the number of observations approaches infinity can be proved under natural conditions