# Supervised Homogeneity Fusion: a Combinatorial Approach

arXiv: https://arxiv.org/abs/2201.01036 · HTML: https://mlsanity.com/paper/2201.01036/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 45 references that are in the map.
- First posted on arXiv 4 Jan 2022.

## Builds on (most cited first, 2 of 2)

- [Best Subset Selection via a Modern Optimization Lens](https://mlsanity.com/paper/1507.03133/) (2015)
- [A concave pairwise fusion approach to subgroup analysis](https://mlsanity.com/paper/1508.07045/) (2015)

## Abstract (arXiv)

Fusing regression coefficients into homogenous groups can unveil those coefficients that share a common value within each group. Such groupwise homogeneity reduces the intrinsic dimension of the parameter space and unleashes sharper statistical accuracy. We propose and investigate a new combinatorial grouping approach called L0-Fusion that is amenable to mixed integer optimization (MIO). On the statistical aspect, we identify a fundamental quantity called grouping sensitivity that underpins the difficulty of recovering the true groups. We show that L0-Fusion achieves grouping consistency under the weakest possible requirement of the grouping sensitivity: if this requirement is violated, then the minimax risk of group misspecification will fail to converge to zero. Moreover, we show that in the high-dimensional regime, one can apply L0-Fusion coupled with a sure screening set of features without any essential loss of statistical efficiency, while reducing the computational cost substantially. On the algorithmic aspect, we provide a MIO formulation for L0-Fusion along with a warm start strategy. Simulation and real data analysis demonstrate that L0-Fusion exhibits superiority over its competitors in terms of grouping accuracy.