SUPERVISED HOMOGENEITY FUSION: A COMBINATORIAL APPROACH

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.