A0674
Title: Conformal uncertainty quantification using kernel depth measures in separable Hilbert spaces
Authors: Marcos Matabuena - Harvard University (Spain) [presenting]
Pavlo Mozharovskyi - Telecom Paris, Institut Polytechnique de Paris (France)
Oscar Hernan Madrid Padilla - UCLA (United States)
Jukka-Pekka Onnela - Harvard University (United States)
Rahul Ghosal - University of South Carolina (United States)
Abstract: Depth measures have gained popularity in the statistical literature for defining level sets in complex data structures like multivariate data, functional data, and graphs. Despite their versatility, integrating depth measures into regression modeling for establishing prediction regions remains underexplored. To address this gap, a novel method is proposed utilizing a model-free uncertainty quantification algorithm based on conditional depth measures and conditional kernel mean embeddings. This enables the creation of tailored prediction and tolerance regions in regression models handling complex statistical responses and predictors in separable Hilbert spaces. The focus is exclusively on examples where the response is a functional data object. To enhance practicality, a conformal prediction algorithm is introduced, providing non-asymptotic guarantees in the derived prediction region. Additionally, both conditional and unconditional consistency results and fast convergence rates are established in some special homoscedastic cases. The model finite sample performance is evaluated in extensive simulation studies with different function objects as probability distributions and functional data. Finally, the approach is applied in a digital health application related to physical activity, aiming to offer personalized recommendations in the U.S. population-based on individuals' characteristics.
