New Deep Learning Framework Regresses Random Objects in Metric Spaces Without Manifold Assumptions
burny_tech · x · 2026-10-24
An arXiv paper by Marcos Matabuena, Xiaokai Luo and Oscar Hernan Madrid Padilla proposes a deep learning framework for regression with random objects in metric spaces, operating directly on the metric structure of the response space and avoiding the restrictive manifold or Euclidean embedding assumptions of existing methods.
- Motivation: modern biomedical outcomes increasingly take the form of probability distributions, random graphs and functions, yet principled non-Euclidean DL methods remain scarce
- Theory: the authors establish statistical consistency and convergence rates, and characterize conditions mitigating the curse of dimensionality for hierarchically compositional regression functions
- Experiments: simulations across Euclidean and non-Euclidean settings show competitive predictive gains
- Application: validated in two digital health case studies with distribution-valued biomarkers
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