A metalearning study for nonlinear robust regression

Abstract

Metalearning is a methodology aiming at recommending the most suitable algorithm (or method) from several alternatives for a par- ticular dataset. Its classification rule is learned over an available training database of datasets. It gradually penetrates to various applications in computer science and has also the potential to recommend the most suitable statistical estimator for a given dataset. We consider the non-linear regression model. While there are some robust alternatives to the traditional (and very non-robust) nonlinear least squares available, it is not theoretically known which estimator performs the best for a partic- ular dataset. In this work, we perform a metalearning study performed over 721 datasets predicting the best nonlinear regression estimator for an independent dataset. The estimators considered here include stan- dard nonlinear least squares as well as its robust alternatives with a high breakdown point. On the whole, the presented study brings new argu- ments in favor of the nonlinear least weighted squares estimator, which is based on the idea to assign implicit weights to individual observations based on outlyingness of their residuals.