Uncertainty quantification in metric spaces

TL;DR

This paper presents a new uncertainty quantification framework for regression models with responses in metric spaces, offering efficient algorithms with theoretical guarantees, demonstrated through clinical applications involving complex data types.

Contribution

It introduces a novel, model-agnostic uncertainty quantification method for metric space responses with asymptotic and non-asymptotic guarantees, applicable to large datasets.

Findings

Algorithms are efficient and scalable to large datasets.

The framework provides asymptotic consistency guarantees.

Successful application to clinical data with complex responses.

Abstract

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.