Paper: arXiv 2212.07944

Authors: Kaizheng Wang, Xiao Xu, Xun Yu Zhou

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.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 6.0/10 (capped from 7.5: transaction costs not modelled; see penalty flags)
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a strong theoretical bridge between distributionally robust optimization and subspace clustering, backed by convex relaxations and an ADMM solver. Empirical validation is solid, featuring both extensive simulation studies and a real-world application to stock returns for portfolio selection.

Research Flowchart

  flowchart TD
    A["Research Goal: Variable Clustering in Multi-Factor Block Models"] --> B["Data & Inputs: Stock Return Data & Synthetic Simulations"]
    B --> C["Methodology: Distributionally Robust Nodewise Regression"]
    C --> D["Convex Relaxation & Data-Driven Parameter Selection"]
    D --> E["Optimization: ADMM Algorithm Implementation"]
    E --> F["Outcomes: Interpretable Stock Clusters & Superior Out-of-Sample Portfolio Selection"]