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Categorical and geometric methods in statistical, manifold, and machine learning

arXiv 2505.03862 ↗First posted 6 May 2025stat.ML cs.LG math.CTcited by 0

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Abstract (arXiv)

We present and discuss applications of the category of probabilistic morphisms, initially developed in citeLe2023, as well as some geometric methods to several classes of problems in statistical, machine and manifold learning which shall be, along with many other topics, considered in depth in the forthcoming book citeLMPT2024.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 5 of its 66 references that are in the map. First posted on arXiv 6 May 2025.

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5 of 66 references.

References · 5

  1. 2021The Modern Mathematics of Deep Learningcited by 63
  2. 2019A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statisticscited by 56
  3. 2014Geodesic Exponential Kernels: When Curvature and Linearity Conflictcited by 47
  4. 2014Kernel Methods on Riemannian Manifolds with Gaussian RBF Kernelscited by 30
  5. 2023Supervised learning with probabilistic morphisms and kernel mean embeddingscited by 1

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