论文信息 - A Minimax Method for Learning Functional Networks

A Minimax Method for Learning Functional Networks

In this paper, a minimax method for learning functional networks is presented. The idea of the method is to minimize themaximum absolute error between predicted and observed values. In addition, the invertible functions appearing in the modelare assumed to be linear convex combinations of invertible functions. This guarantees the invertibilityof the resulting approximations. The learning method leads to a linear programming problem and then: (a) the solution isobtained in a finite number of iterations, and (b) the global optimum is attained. The method is illustrated withseveral examples of applications, including the Hénon and Lozi series. The results show that the method outperforms standard least squares direct methods.

[1] Enrique Castillo,et al. Functional equations and modelling in science and engineering , 1992 .

[2] E. Castillo,et al. Working with differential, functional and difference equations using functional networks , 1999 .

[3] Enrique Castillo,et al. Functional Networks , 1998, Neural Processing Letters.

[4] Hal S. Stern,et al. Neural networks in applied statistics , 1996 .

[5] J. Aczél,et al. Lectures on Functional Equations and Their Applications , 1968 .

[6] M. Hénon,et al. A two-dimensional mapping with a strange attractor , 1976 .

[7] Enrique Castillo,et al. Nonlinear time series modeling and prediction using functional networks. Extracting information masked by chaos , 1998 .

[8] William H. Press,et al. Numerical Recipes in C, 2nd Edition , 1992 .

[9] E. Castillo,et al. Functional Networks: A New Network‐Based Methodology , 2000 .