  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.
