# Estimating Regression Function with $\varepsilon-Insensitive$ Supervised Learning Algorithm

• Hwang, Chang-Ha (Dept. of Statistical Information, Catholic University of Daegu)
• Published : 2004.05.31

#### Abstract

One of the major paradigms for supervised learning in neural network community is back-propagation learning. The standard implementations of back-propagation learning are optimal under the assumptions of identical and independent Gaussian noise. In this paper, for regression function estimation, we introduce $\varepsilon-insensitive$ back-propagation learning algorithm, which corresponds to minimizing the least absolute error. We compare this algorithm with support vector machine(SVM), which is another $\varepsilon-insensitive$ supervised learning algorithm and has been very successful in pattern recognition and function estimation problems. For comparison, we consider a more realistic model would allow the noise variance itself to depend on the input variables.