Distance based modeling of interactions in structured regression

Abstract

Graphical models, as applied to multi-target prediction problems, commonly utilize interaction terms to impose structure among the output variables. Often, such structure is based on the assumption that related outputs need to be similar and interaction terms that force them to be closer are adopted. Here we relax that assumption and propose a feature that is based on distance and can adapt to ensure that variables have smaller or larger difference in values. We utilized a Gaussian Conditional Random Field model, where we have extended its originally proposed interaction potential to include a distance term. The extended model is compared to the baseline in various structured regression setups. An increase in predictive accuracy was observed on both synthetic examples and real-world applications, including challenging tasks from climate and healthcare domains.