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SUPERVISED HOMOGENEITY FUSION: A COMBINATORIAL APPROACH.

Wen Wang¹, Shihao Wu², Ziwei Zhu²

¹Department of Biostatistics, University of Michigan, Ann Arbor.

Annals of Statistics

|August 7, 2025

Summary

This summary is machine-generated.

L0-Fusion groups regression coefficients for enhanced statistical accuracy. This novel combinatorial approach achieves grouping consistency with minimal sensitivity requirements, outperforming competitors in accuracy.

Keywords:

Clustering dimension reduction linear model mixed integer optimization supervised learning

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Area of Science:

Statistics
Machine Learning
Optimization

Background:

Grouping regression coefficients reduces parameter space dimensionality.
Homogeneous groups enhance statistical accuracy and model interpretability.

Purpose of the Study:

Introduce L0-Fusion, a novel combinatorial grouping approach for regression coefficients.
Investigate the statistical properties and algorithmic aspects of L0-Fusion.
Demonstrate the superiority of L0-Fusion over existing methods.

Main Methods:

Developed a mixed integer optimization (MIO) formulation for L0-Fusion.
Introduced and analyzed 'MSE grouping sensitivity' to quantify grouping difficulty.
Proposed a warm start strategy for the MIO algorithm.

Main Results:

L0-Fusion achieves grouping consistency under minimal MSE grouping sensitivity.
The method maintains statistical efficiency in high-dimensional settings with feature screening.
Simulations and real data show improved grouping accuracy compared to competitors.

Conclusions:

L0-Fusion offers a statistically robust and computationally efficient method for coefficient grouping.
The approach provides theoretical guarantees for grouping consistency.
L0-Fusion represents a significant advancement in statistical modeling and parameter estimation.