Interval-Valued Regression - Sensitivity to Data Set Features

Regression represents one of the most basic building blocks of data analysis and AI. Despite growing interest in interval-valued data across various fields, approaches to establish regression models for interval-valued data which address and handle the specific properties of given data sets are very limited. For broader use and adoption of regression for intervals, this paper conducts a sensitivity analysis of key extant linear regression approaches in respect to important features of interval-valued data sets, such as the mean and associated standard deviation of the range (size) of the intervals within the data set-a measure of overall size and size-diversity, and the dispersion of interval-centers-a measure of diversity in terms of interval position. Experiments with carefully designed synthetic exemplar data sets with these properties suggest that distant placement of intervals as well as higher standard deviation (uncertainty) of ranges increase estimation errors; that is, they result in lower linear regression model fitness for all regression methods as may intuitively be expected. However, these errors are lower for the best suited Parameterized model in comparison to the MinMax and Constrained Center and Range methods. This paper sheds light on the behaviour and 'expectable' performance of key linear regression models designed for interval-valued data and adds a further building block to supporting the broader adoption of intervals (and subsequently fuzzy sets) as a fundamental data type in AI.