Variable Clustering via Distributionally Robust Nodewise Regression

TL;DR

This paper introduces a distributionally robust nodewise regression approach for variable clustering, connecting multi-factor block models with regularized subspace clustering, and demonstrates its effectiveness through simulations and stock data analysis.

Contribution

It develops a convex relaxation and ADMM algorithm for robust variable clustering, with guidance on selecting regularization parameters based on data.

Findings

The method accurately identifies variable clusters in simulations.

It produces interpretable clusters that aid portfolio selection.

Outperforms other clustering methods in empirical stock data analysis.

Abstract

We study a multi-factor block model for variable clustering and connect it to the regularized subspace clustering by formulating a distributionally robust version of the nodewise regression. To solve the latter problem, we derive a convex relaxation, provide guidance on selecting the size of the robust region, and hence the regularization weighting parameter, based on the data, and propose an ADMM algorithm for implementation. We validate our method in an extensive simulation study. Finally, we propose and apply a variant of our method to stock return data, obtain interpretable clusters that facilitate portfolio selection and compare its out-of-sample performance with other clustering methods in an empirical study.