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arXiv · 2412.13122

Fr\'echet Sufficient Dimension Reduction for Metric Space-Valued Data via Distance Covariance

Hsin-Hsiung Huang·Feng Yu·Kang Li·Teng Zhang
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Abstract

We propose a novel Fr\'echet sufficient dimension reduction (SDR) method based on kernel distance covariance, tailored for metric space-valued responses such as count data, probability densities, and other complex structures. The method leverages a kernel-based transformation to map metric space-valued responses into a feature space, enabling efficient dimension reduction. By incorporating kernel distance covariance, the proposed approach offers enhanced flexibility and adaptability for datasets with diverse and non-Euclidean characteristics. The effectiveness of the method is demonstrated through synthetic simulations and several real-world applications. In all cases, the proposed method runs faster and consistently outperforms the existing Fr\'echet SDR approaches, demonstrating its broad applicability and robustness in addressing complex data challenges.

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Hsin-Hsiung Huang, Feng Yu, Kang Li, Teng Zhang. 2024-12-17. Fr\'echet Sufficient Dimension Reduction for Metric Space-Valued Data via Distance Covariance. https://arxiv.org/abs/2412.13122

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