Polynomials have shown to be useful basis functions in the identification of nonlinear systems. However estimation of the unknown coefficients requires expensive algorithms, as for instance it occurs by applying an optimal least square approach. Bernstein polynomials have the property that the coefficients are the values of the function to be approximated at points in a fixed grid, thus avoiding a time-consuming training stage. This paper presents a novel machine learning approach to regression, based on new functions named particle-Bernstein polynomials, which is particularly suitable to solve multivariate regression problems. Several experimental results show the validity of the technique for the identification of nonlinear systems and the better performance achieved with respect to the standard techniques.
Machine learning regression based on particle Bernstein polynomials for nonlinear system identification / Biagetti, Giorgio; Crippa, Paolo; Falaschetti, Laura; Turchetti, Claudio. - ELETTRONICO. - (2017), pp. 1-6. (Intervento presentato al convegno 2017 IEEE 27th International Workshop on Machine Learning for Signal Processing (MLSP) tenutosi a Tokyo, Japan nel 25-28 Sept. 2017) [10.1109/MLSP.2017.8168148].