Work

Sparse Fréchet sufficient dimension reduction with graphical structure among predictors

Year: 2025

Type: article

Abstract: Fréchet regression has received considerable attention to model metric‐space valued responses that are complex and non‐Euclidean data, such as probability distributions and vectors on the unit sphere. However, existing Fréchet regression literature focuses on the classical setting where the predictor dimension is fixed, and the sample size goes to infinity. This paper proposes sparse Fréchet sufficient dimension reduction with graphical structure among high‐dimensional Euclidean predictors. In particular, we propose a convex optimization problem that leverages the graphical information among predictors and avoids inverting the high‐dimensional covariance matrix. We also provide the Alternating Direction Method of Multipliers (ADMM) algorithm to solve the optimization problem. Theoretically, the proposed method achieves subspace estimation and variable selection consistency under suitable conditions. Extensive simulations and a real data analysis are carried out to illustrate the finite‐sample performance of the proposed method.

Source: Scandinavian Journal of Statistics

DOI: 10.1111/sjos.12791

Authors: Jiaying Weng, Kai Tan, Cheng Wang, Zhou Yu

Institutions: Bentley University, Rutgers, The State University of New Jersey, Shanghai Jiao Tong University, East China Normal University

Language: English

Topic: Statistical Methods and Inference

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,500

Funders: Major Research Plan, National Key Research and Development Program of China