doiSerbia

Sparse regularized fuzzy regression

Rapaić Danilo (University of Novi Sad, Faculty of Technical Sciences, Novi Sad, Serbia)
Krstanović Lidija (University of Novi Sad, Faculty of Technical Sciences, Department of Fundamentals Sciences, Chair of Engineering Animation, Novi Sad, Serbia)
Ralević Nebojša (University of Novi Sad, Faculty of Technical Sciences, Novi Sad, Serbia)
Obradović Ratko (University of Novi Sad, Faculty of Technical Sciences, Department of Fundamentals Sciences, Chair of Engineering Animation, Novi Sad, Serbia)
Klipa Đuro (University of Novi Sad, Faculty of Technical Sciences, Novi Sad, Serbia)

In this work, we focus on two things: First, in addition to the data measurement uncertainty, we develop a novel probabilistic model by imposing the additive noise in the classical fuzzy regression model. We obtain the baseline LS estimation as the maximum likelihood estimation for regression parameters. Moreover, by assuming the heavy tail distribution and by introducing the Huber norm instead of square in the cost function, we obtain more general robust fuzzy M-estimator, much more suitable for modeling the outliers often present in the data sets.

Keywords: Fuzzy regression, sparse regularization, Huber norm, robust statistics, MAP estimate