21st EANN 2020, 5 -7 June 2020, Greece

A Metalearning Study for Robust Nonlinear Regression

Jan Kalina, Petra Vidnerov√°


  Metalearning is a methodology aiming at recommending the most suitable algorithm (or method) from several alternatives for a particular 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 nonlinear 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 particular 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 standard nonlinear least squares as well as its robust alternatives with a high breakdown point. On the whole, the presented study brings new arguments 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.  

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