Hyperbolic regression: a new regression model with applications to the binary classification problem

Abstract

This paper proposes a new regression model in which the outcome variables are restricted to values in the interval [0,1] or also to values measured on a binary scale, when the model can be used for the binary classification problem. The name hyperbolic regression was given because the model originated from the hyperbolic penalty method. More precisely, a parameterization of the derivative of the hyperbolic penalty function is proposed for the construction of the regression model. The coefficients of the hyperbolic regression model can be obtained by either the least squares or the maximum likelihood methods. The hyperbolic regression belongs to the class of generalized linear models and has similarities with the logistic regression. Thus, a comparison of the logistic and hyperbolic regression models is presented. To illustrate the efficiency of the method, a set of computational experiments is performed, making use of the traditional instances described in the literature. In almost all experiments, the hyperbolic regression had lower residues as well as greater accuracy and F1 score than the logistic regression. Thus, the proposed model can be very promising for regressions and binary classification tasks.