arXiv:2609.27766v1 Announce Type: cross
Abstract: In safe hypothesis testing with test supermartingals, Ville's inequality provides anytime-valid type-I error guarantees for every significance level...
By Patrick Forr\'e
The paper proves that in time‑series validation three desirable properties—training sufficiency, test coverage, and temporal causality—cannot all be satisfied simultaneously. It introduces quantitative bounds involving the smallest training fraction (α), test coverage (β), future training fraction (Λ), and distance to nearest future training point (δ), showing that exceeding the causal frontier α+β=1 requires training on future data that must lie within (1−α)T of a test point. The authors demonstrate that the impact of such future leakage depends on distance rather than amount, and compare different validation schemes (walk‑forward, k‑fold, purged k‑fold) in terms of their position on this Pareto frontier, illustrating the trade‑offs with empirical results on noise data.
By Jiayu Li
The paper introduces a two-player zero-sum repeated game between a learner and nature that simultaneously captures Bayesian updating and an exact decomposition of exponential-weights regret. The game’s terminal payoff reflects the maximum gain a comparator can achieve given a fixed relative entropy from the prior, while the one-step constraint limits nature’s move by an information budget. The resulting regret splits into three precise components—per-round information loss, an additive retempering drift, and the comparator’s information relative to the prior—providing a unified framework that explains concentration phenomena, large-deviation bounds, and various learning methods such as bandits, posterior sampling, aggregation, and boosting.
By Akshay Balsubramani
arXiv:2608. 09450v1 Announce Type: new Abstract: Betting-based sequential tests and Blackwell approachability are linked by a rate-explicit reduction through support-function residuals.
By Jinze Zhao
arXiv:2509. 11208v3 Announce Type: replace-cross Abstract: Transformers used for evidence-grounded binary adjudication (e.
By Leon Chlon, Ahmed Karim, Maggie Chlon, MarcAntonio Awada
arXiv:2606. 08517v1 Announce Type: new Abstract: Selective predictors answer on confident inputs and abstain elsewhere; deploying one safely needs a single finite-sample certificate that simultaneously upper-bounds the selected risk, lower-bounds the acceptance probability $\pacc$ above a floor $\pmin$, and lower-bounds the deployment utility.
By Xiaoli Yu, Jiamiao Liu