mlsanityData to 7 Oct 2026

Uncertainty quantification in metric spaces

arXiv 2405.05110 ↗First posted 8 May 2024math.ST stat.ML stat.THcited by 3

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Abstract (arXiv)

This paper introduces a novel uncertainty quantification framework for regression models where the response takes values in a separable metric space, and the predictors are in a Euclidean space. The proposed algorithms can efficiently handle large datasets and are agnostic to the predictive base model used. Furthermore, the algorithms possess asymptotic consistency guarantees and, in some special homoscedastic cases, we provide non-asymptotic guarantees. To illustrate the effectiveness of the proposed uncertainty quantification framework, we use a linear regression model for metric responses (known as the global Fr'echet model) in various clinical applications related to precision and digital medicine. The different clinical outcomes analyzed are represented as complex statistical objects, including multivariate Euclidean data, Laplacian graphs, and probability distributions.

Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 61 of its 137 references that are in the map. First posted on arXiv 8 May 2024.

Builds on

61 of 137 references.

References · 61

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38 more
  1. 2020Conformal prediction for time seriescited by 53
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Citing papers per year: 2025: 3.

3 papers.

  1. 2025Conformal and kNN Predictive Uncertainty Quantification Algorithms in Metric Spacescited by 2
  2. 2025Variable Selection Methods for Multivariate, Functional, and Complex Biomedical Data in the AI Agecited by 0
  3. 2025Continuous Temporal Learning of Probability Distributions via Neural ODEs with Applications in Continuous Glucose Monitoring Datacited by 0