提出新方法处理复杂结构数据的梯度提升，突破传统算法限制。
Fréchet Geodesic Boosting
- 用测地线替代残差，适配非欧几何输出空间
- 在真实数据和模拟实验中表现优于传统方法
- 适合处理分布、网络等复杂结构数据的研究者
梯度提升已成为机器学习的核心技术，使决策树等基学习器实现优异预测性能。然而现有算法主要针对标量或欧几里得空间输出，面对日益普遍的复杂结构数据（如分布、网络、流形值输出）时面临挑战。这类非欧数据缺乏加减乘除等代数结构，无法直接适用标准梯度提升框架。为此，本文提出适用于测地度量空间输出的弗雷歇测地线提升（Fréchet Geodesic Boosting, FGBoost）方法。该方法以测地线作为残差代理，在输出空间的内在几何结构下构建集成模型。通过理论分析、大量仿真及真实世界应用验证，证明了FGBoost具有强大性能与良好适应性，展现出建模复杂数据的巨大潜力。
原文摘要 · Abstract (English)
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 Fréchet 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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