A0266
Title: Breaking the dimensionality barrier: Frechet sufficient dimension reduction for metric space-valued data
Authors: Hsin-Hsiung Huang - University of Central Florida (United States) [presenting]
Abstract: The rapid emergence of metric space-valued data, including probability distributions, gene expression profiles, and count responses, presents unique challenges to traditional statistical methods, particularly in high-dimensional settings. An innovative Frechet sufficient dimension reduction (FSDR) method is introduced based on kernel distance covariance, designed to address these challenges. The method leverages kernel-based transformations to map metric space-valued responses into feature spaces, enabling efficient dimension reduction while preserving essential data structures. Compared to existing approaches, FSDR demonstrates computational efficiency, flexibility in handling non-Euclidean data, and robustness in diverse applications. Through comprehensive theoretical guarantees, including convergence and consistency, and extensive evaluations on both synthetic and real-world datasets, such as bike rental frequencies and carcinoma gene expression profiles, the proposed method consistently outperforms traditional SDR techniques. By unifying metric-space data analysis with advanced dimensionality reduction, FSDR offers a powerful framework for tackling the complexities of modern data challenges. Attendees gain insights into the methodology, its theoretical underpinnings, and its practical applications in real-world scenarios.
