Linear Regression Models for Interval-Valued Data using Log-transformation

Abstract

—Solving linear regression problems on interval- valued data is a challenging task that may arise in many applications. Because of that, many researchers have designed methods for such task in recent years. Although much effort has been devoted to this problem, all available methods rely on modeling the problem as a constrained optimization task, which may lead to sub-optimal results. Moreover, no previous work provide a way to train a model in a incremental way, which is fundamental for big data problems. In this paper, we address both problems by proposing two different linear regression methods based on log-transformations. The proposed methods, referred as Log-transformed OLS for interval data (LOID) and Log-transformed LMS for interval data (LLID), are compared to state-of-the-art methods on both synthetic and real-world datasets. The obtained results indicate the feasibility of our approaches. Furthermore, to the best of our knowledge, LLID is the first sequential linear regression method for interval valued.