A New Framework for Evaluating the Validity and the Performance of Binary Decisions on Manifold-Valued Data
Résumé
In this paper, we introduce a new framework that can be used
for evaluating the validity and the performance of machine learning models on manifold-valued data. More particularly, two methods are detailed
with theoretical properties for spherical and functional data. In a general
setting, we develop a new set of procedures for nonparametric hypothesis
testing on manifolds within a desired error level. These tests encompass
probability distributions constrained to specific domains, which can pose
significant challenges for commonly used techniques. The resulting statistical concepts are primarily characterized by computational simplicity
and are grounded in relevant contexts, making them extendable to a wide
range of applications. The algorithms and the theoretical analysis of the
proposed methods are substantiated by many and varied experimental
results on simulated and real data.