Hsin-Hsiung Huang : Low-Rank Distance Covariance for Fréchet Sufficient Dimension Reduction in High-Dimensional Functional Data

Posted by Kyunghee Han , part of the Statistics and Data Science Seminar.

At

April 1, 2026, 4:15 p.m.

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636 SEO

Abstract

We develop a new Fréchet sufficient dimension reduction (FdSDR) framework tailored for high-dimensional functional data with complex, metric-space-valued responses. Our main contribution is a low-rank distance covariance criterion that enables scalable, model-free identification of low-dimensional predictor structures while capturing nonlinear dependence. The proposed method is computationally efficient in high dimensions and avoids restrictive distributional assumptions. We establish theoretical guarantees and demonstrate its effectiveness through simulations and real data, providing a practical and flexible approach for modern functional data analysis.