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Conformal uncertainty quantification using kernel depth measures in separable Hilbert spaces by Matabuena, Marcos; Ghosal, Rahul; Mozharovskyi, Pavlo; Padilla, Oscar Hernan Madrid; Onnela, Jukka-Pekka is a scholarly article available to read on EtoBox.

What is Conformal uncertainty quantification using kernel depth measures in separable Hilbert spaces about?

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, we propose a novel method 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. Our focus in this paper is exclusively on examples where the response is a functional data object. To enhance practicality, we introduce a conformal prediction algorithm, providing non-asymptotic guarantees in the derived prediction region. Additionally, we establish both conditional and unconditional consistency results and fast convergence rates in some special homoscedastic cases. We evaluate the model finite sample performance in extensive simulation studies with different function objects as probability distributions and

Author

Matabuena, Marcos; Ghosal, Rahul; Mozharovskyi, Pavlo; Padilla, Oscar Hernan Madrid; Onnela, Jukka-Pekka

Published

2024

Language

EN