🤖 AI Summary
Existing conformal prediction theory relies on deterministic nonconformity measures, which are ill-suited for machine learning settings involving randomness. Moreover, the commonly adopted condition of exchangeability in distribution is insufficient to guarantee valid predictions in such stochastic contexts. This work addresses these limitations by introducing a stricter sufficient condition for validity—combining conditional independence with distributional exchangeability—and develops a novel conformal prediction framework grounded in probability theory and statistical learning theory. The proposed approach establishes rigorous validity conditions applicable to a broad class of randomized machine learning procedures, thereby providing a solid theoretical foundation for practical applications involving stochastic training processes.
📝 Abstract
The theory of full conformal prediction uses deterministic non-conformity measure, but modern usage of full conformal prediction often relies on machine learning training, making stochasticity inevitable. A simple sufficient condition of almost sure permutation invariance of the non-conformity measure can be too restrictive, so many have suggested the relaxation to permutation in distribution as a condition for full conformal prediction validity. We, however, show that this commonly known condition is actually insufficient. We then provide a correct sufficient condition: Conditional Independence & Permutation Invariance in Distribution, which encompasses several stochastic settings that may be used in machine learning.