Metric Conformal Prediction via the Conditional Expected Local Radius
Read the original on arXiv Machine Learning →The paper introduces the conditional expected local radius (CELR), a new tool for measuring local conditional probability concentration in general metric spaces. Using CELR, the authors develop a conformal prediction method that works for non‑Euclidean responses, accommodates heterogeneity and multimodality without requiring densities or vector‑space structure, and avoids costly transport comparisons. The method is implemented via a metric distributional random forest that handles multivariate covariates and nonlinear interactions, yielding uniform consistency, asymptotic conditional validity, and finite‑sample marginal coverage under exchangeability, while also providing substantial computational savings compared to existing approaches.
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