Fr\'echet Geodesic Boosting

Yidong Zhou; Su I Iao; Hans-Georg Müller

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arXiv · 2509.18013

Fr\'echet Geodesic Boosting

Yidong Zhou·Su I Iao·Hans-Georg Müller

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Abstract

Gradient boosting has become a cornerstone of machine learning, enabling base learners such as decision trees to achieve exceptional predictive performance. While existing algorithms primarily handle scalar or Euclidean outputs, increasingly prevalent complex-structured data, such as distributions, networks, and manifold-valued outputs, present challenges for traditional methods. Such non-Euclidean data lack algebraic structures such as addition, subtraction, or scalar multiplication required by standard gradient boosting frameworks. To address these challenges, we introduce Fr\'echet geodesic boosting (FGBoost), a novel approach tailored for outputs residing in geodesic metric spaces. FGBoost leverages geodesics as proxies for residuals and constructs ensembles in a way that respects the intrinsic geometry of the output space. Through theoretical analysis, extensive simulations, and real-world applications, we demonstrate the strong performance and adaptability of FGBoost, showcasing its potential for modeling complex data.

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Yidong Zhou, Su I Iao, Hans-Georg Müller. 2025-09-22. Fr\'echet Geodesic Boosting. https://arxiv.org/abs/2509.18013

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