Fréchet Geodesic Boosting
This addresses a problem for machine learning practitioners dealing with complex data types, offering a novel method rather than an incremental improvement.
The paper tackles the challenge of gradient boosting for complex-structured, non-Euclidean data like distributions and manifolds by introducing Fréchet geodesic boosting (FGBoost), which uses geodesics as residuals and respects intrinsic geometry, demonstrating strong performance in simulations and applications.
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.