PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Support Vector Regression for the Simultaneous Learning of a Multivariate Function and its Derivatives
Marcelino Lazaro, Ignacio Santamaria, Fernando Perez-Cruz and Antonio Artes
NeuroComputing 2003.

Abstract

In this paper, the problem of simultaneously approximating a function and its derivatives is formulated within the Support Vector Machine (SVM) framework. First, the problem is solved for a one-dimensional input space by using the ε-insensitive loss function and introducing additional constraints in the approximation of the derivative. Then, we extend the method to multi-dimensional input spaces by a multidimensional regression algorithm. In both cases, to optimize the regression estimation problem, we have derived an iterative re-weighted least squares (IRWLS) procedure that works fast for moderate-size problems. The proposed method shows that using the information about derivatives significantly improves the reconstruction of the function.

EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:1177
Deposited By:Fernando Perez-Cruz
Deposited On:19 November 2005