Supervised Homogeneity Fusion: a Combinatorial Approach

Identifying homogeneous groups of regression coefficients has received increasing attention because the resulting regression model provides better scientific interpretations and enhance predictive performance in many applications. In some occasions, features or covariates naturally act in groups to influence outcomes, so knowing group structures of the features help scientists gain new knowledge about a physical system of interest. From a modeling perspective, aggregating covariates with similar effects along with the response reduces model complexity and improves interpretability, especially in the highdimensional regime. There have been a flurry of works under this direction; see for example Bondell and Reich (2008); Shen and Huang (2010); Zhu, Shen and Pan (2013); Ke, Fan and Wu (2015); Jeon, Kwon and Choi (2017), among others. There is a vast literature in discovering homogeneous groups of observations or individuals in overly heterogeneous population. However, these existing methods cannot be applied to our problem that aims to group regression parameters.