Monte Carlo testing: non-asymptotic guarantees without joint exchangeability

arXiv:2607.23010 2026 Theory 1 ideas extracted · analyzed Aug 30, 2026

What the math gives to ML

The paper gives a finite-sample method for using dependent Monte Carlo replicas when joint exchangeability and MCMC mixing are unavailable. Its transferable asset is a conditional-i.i.d. coupling: if the observed sample and each simulated copy are conditionally independent given a latent variable, the empirical rank p-value remains conservative up to an explicit factor of two, regardless of the number of replicas or chain mixing. This can provide a principled audit and early-stopping signal for neural generative models, posterior-predictive models, and learned samplers, provided the neural test statistic is frozen independently of the evaluation data.

Ideas from this paper

Unverified 2026

Factor-Two Neural Model-Criticism Test

Use a frozen neural discrepancy score and conditional Monte Carlo replicas to test whether a generative model or learned sampler is compatible with a null data distribution, without requiring mixed chains or joint exchangeability. The resulting empirical p-value has a finite-sample false-alarm bound of at most two times the nominal level, making it safer than an ordinary Monte Carlo rank test for validation and deployment monitoring.

Useful5/10
Difficulty4/10
Novelty7/10
Paper: Monte Carlo testing: non-asymptotic guarantees without joint exchangeability arXiv:2607.23010