KOO Method-based Consistent Clustering for Group-wise Linear Regression with Graph Structure

2025/09/14 by Ohishi, M., Oda, R.
#62J05 #FOS: Computer and information sciences #G.3 #Methodology (stat.ME)

paper · doi:10.48550/arxiv.2509.11103

Abstract

The kick-one-out (KOO) method is a variable selection method based on a model selection criterion. The method is very simple, and yet it has consistency in variable selection under a high-dimensional asymptotic framework with a specific model selection criterion. This paper proposes the join-twotogether (JTT) method, which is a clustering method based on the KOO method for group-wise linear regression with graph structure. The JTT method formulates the clustering problem as an edge selection problem for a graph and determines whether to select each edge based on the KOO method. We can employ network Lasso to perform such a clustering. However, network Lasso is somewhat cumbersome because there is no good algorithm for solving the associated optimization problem and the tuning is complicated. Therefore, by deriving a model selection criterion such that the JTT method has consistency in clustering under a high-dimensional asymptotic framework, we propose a simple yet powerful method that outperforms network Lasso.

Citations

• Strong consistency of the AIC, BIC, C_p and KOO methods in high-dimensional multivariate linear regression
• Estimating the Dimension of a Model

Related

• Efficient Path Algorithms for Clustered Lasso and OSCAR
• Efficient Clustering of Correlated Variables and Variable Selection in High-Dimensional Linear Models
• Clustered regression with unknown clusters
• flow-based clustering and spectral clustering: a comparison
• Advanced Graph Clustering Methods: A Comprehensive and In-Depth Analysis