A Restricted Parametrized Model for Interval-Valued Regression

This paper explores the parameter generation of the existing ‘Parametrized Model’ (PM) as the state-of-the-art linear interval-valued regression model, highlighting that its strong performance may arise from unexpected behavior. Focusing on the approach's core idea of using dynamic reference points from the regressor variables to describe and regress interval-valued data, this paper shows that key parameters in the PM method are not actually restricted, and explores the impact this has on model generation. As part of this analysis, we propose a Restricted Parametrized Model (RPM) which ensures parameter bounds are maintained. We evaluate the approach by conducting linear regression for a series of synthetic interval-valued data sets with different features, discussing its performance against the original PM and other linear interval regression models. The experiments confirm empirically that the PM model violates restrictions on parameter bounds, resulting in the selection of reference points—outside—the regressor intervals–nevertheless producing strongly performing regression models which outperform other models, including RPM, when parameter bounds are violated. We conclude by discussing that the mechanism underpinning the PM regression is different to what is expected, i.e. it commonly selects reference points which are not from the regressor variables, warranting further research to explore whether the PM's parameter bounds can be relaxed, or whether this exposes potential problems, for example for edge cases.