Conformal uncertainty quantification using kernel depth measures in separable Hilbert spaces

• DOI: 10.48550/arxiv.2405.13970
• Publication Date: 2024-05-22
• Authors: Marcos Matabuena; Rahul Ghosal; Pavlo Mozharovskyi; Oscar Hernán Madr...; Jukka‐Pekka Onnela
• Keywords: Kernel (algebra)

Depth measures have gained popularity in the statistical literature for defining level sets complex data structures like multivariate data, functional and graphs. Despite their versatility, integrating depth into regression modeling establishing prediction regions remains underexplored. To address this gap, we propose a novel method utilizing model-free uncertainty quantification algorithm based on conditional kernel mean embeddings. This enables creation of tailored tolerance models handling responses predictors separable Hilbert spaces. Our focus paper is exclusively examples where response object. enhance practicality, introduce conformal algorithm, providing non-asymptotic guarantees derived region. Additionally, establish both unconditional consistency results fast convergence rates some special homoscedastic cases. We evaluate model finite sample performance extensive simulation studies with different function objects as probability distributions data. Finally, apply approach digital health application related to physical activity, aiming offer personalized recommendations US. population individuals' characteristics.