Nonparametric nonlinear regression using polynomial and neural approximators: a numerical comparison

Abstract

The solution of nonparametric regression problems is addressed via polynomial approximators and one-hidden-layer feedforward neural approximators. Such families of approximating functions are compared as to both complexity and experimental performances in finding a nonparametric mapping that interpolates a finite set of samples according to the empirical risk minimization approach. The theoretical background that is necessary to interpret the numerical results is presented. Two simulation case studies are analyzed to fully understand the practical issues that may arise in solving such problems. The issues depend on both the approximation capabilities of the approximating functions and the effectiveness of the methodologies that are available to select the tuning parameters, i.e., the coefficients of the polynomials and the weights of the neural networks. The simulation results show that the neural approximators perform better than the polynomial ones with the same number of parameters. However, this superiority can be jeopardized by the presence of local minima, which affects the neural networks but does not regard the polynomial approach

RETRACTED ARTICLE: Machine learning-based self-sensing of the stiffness of shape memory coil actuator

“…These two phases have different crystallographic structures but with the same chemical composition, atomic weight, and mass number. The Feedforward Neural Network (FFNN) model is compared with the classical regression polynomial model and the results obtained from FFNN are promising (Alessandri et al 2009 ).…”

“…The appropriate mathematical model of sensor characteristics can be obtained by curve fitting (Jiang et al 2021 ). The comparison between classical polynomial regression and Feedforward Neural Network (FFNN) methods of modeling concludes that complicated interaction function can be better model by the FFNN method (Alessandri et al 2009 ). The Neural Network universal approximator which is performing better than polynomial regression explained correctly in Szemenyei and Estivill-Castro ( 2021 ).…”

“…The different curve fitting equations are used to model the sensor characteristics and determine the best out of it for calibration in Jiang et al ( 2021 ). Any mathematical function can be modeled by universal approximator (FFNN) and it is called white box modeling in Alessandri et al ( 2009 ). But, it could not explain how to optimize it.…”

Machine Learning based Self-sensing the Stiffness of Shape Memory Coil Actuator

“…These two phases have different crystallographic structures but with the same chemical composition, atomic weight, and mass number. The Feedforward Neural Network (FFNN) model is compared with the classical regression polynomial model and the results obtained from FFNN are promising (Angelo Alessandri et al 2009).…”