Regression Models for Symbolic Interval-Valued Variables

Abstract

This paper presents new approaches to fit regression models for symbolic internal-valued variables, which are shown to improve and extend the center method suggested by Billard and Diday and the center and range method proposed by Lima-Neto, E.A.and De Carvalho, F.A.T. Like the previously mentioned methods, the proposed regression models consider the midpoints and half of the length of the intervals as additional variables. We considered various methods to fit the regression models, including tree-based models, K-nearest neighbors, support vector machines, and neural networks. The approaches proposed in this paper were applied to a real dataset and to synthetic datasets generated with linear and nonlinear relations. For an evaluation of the methods, the root-mean-squared error and the correlation coefficient were used. The methods presented herein are available in the the RSDA package written in the R language, which can be installed from CRAN.

Interval-valued Data Analysis: A Review

“…During the experimental evaluation, the authors discovered that using nonlinear methods greatly improved prediction results in regression problems. Furthermore, when compared to other methods, particularly those based on linear methods, a simple ANN was able to significantly improve predictions [10].…”

“…Linear and nonlinear regression were used for prediction tasks. However, it has been proven that nonlinear regression methods are superior to linear methods [10,17].…”

“…Table 1 shows the cardio logical interval dataset taken from [10]. The dataset contains 44 rows, and five attributes were recorded as intervals for each patient: pulse rate (Pulse), diastolic blood pressure (Diast), systolic blood pressure (Sys), Art1 and Art2.…”

A Robust Approach to CCRM Interval Regression considering Interval Coincidence Degree

“…en, a novel nonlinear programming model can be presented, in which the maximization of the coincidence degree between observation i and its prediction, as well as the minimization of the overall fitting error are both realized. Mathematically, the objective can be written as formula (13).…”

“…Zhong et al [12] were focused on the bias-corrected and heteroscedasticity-adjusted modeling technique by imposing order constraint to the endpoints of the response interval and the weighted linear least squares with estimated covariance matrix. Chacon and Rodriguez [13] presented a new approach to fit regression model for the symbolic internal-valued variables, which was essentially an improved and extended method for the center method proposed by Billard and Diday [9]. Lim [14] constructed a nonparametric interval regression model with an unknown smoothing function, and a backfitting algorithm was used to estimate the regression coefficients.…”