Bounded Difference Concentration for Infinitely Exchangeable Sequences with Applications to AI Benchmark Uncertainty

Abstract:We consider the concentration properties of functions of infinitely exchangeable random variables. By conditioning on the de Finetti directing measure, we show that the deviation of any function with bounded-difference constants $c_1, \dots, c_n$ decomposes into a conditional sampling fluctuation and a latent mixture fluctuation. When this latent mixture is $\sigma_{\mathrm{mix}}^2$-subgaussian, we establish a concentration inequality with an effective variance proxy of $\frac{1}{4}\sum_i c_i^2 + \sigma_{\mathrm{mix}}^2$. Crucially, we demonstrate that for zero-sum linear contrasts, such as the difference between a subsample mean and a full population mean, the latent mixture term cancels exactly. This cancellation yields a tight, mixture-free Hoeffding-type bound that provides a direct de Finetti mechanism for the infinite-extendibility limit of recent finite-exchangeable concentration results. We apply this framework to quantify uncertainty in composite AI benchmarks, such as MMLU, where question items naturally exhibit exchangeable dependence across domains. Our results provide both a domain-stratified hierarchical model for bounding the uncertainty of accuracy scores, and a distribution-free, cost-saving statistical guarantee for accurately estimating full benchmark scores from random subsets.

Machine Learning (stat.ML); Machine Learning (cs.LG); Probability (math.PR)

arXiv:2606.17426 [stat.ML]

(or arXiv:2606.17426v1 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2606.17426 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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