{"ID":2867840,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.18013","arxiv_id":"2509.18013","title":"Fréchet Geodesic Boosting","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 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.","short_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 manifo...","url_abs":"https://arxiv.org/abs/2509.18013","url_pdf":"https://arxiv.org/pdf/2509.18013v1","authors":"[\"Yidong Zhou\",\"Su I Iao\",\"Hans-Georg Müller\"]","published":"2025-09-22T16:53:27Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.LG\",\"stat.ME\"]","methods":"[]","has_code":false}