arXiv Statistics ML By Fabian Denoodt, Sibylle Hess, Joaquin Vanschoren, Christian A. Naesseth

On the Tightness and Computational Tractability of Higher-Dimensional Confidence Sequences

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The paper investigates higher-dimensional confidence sequences for monitoring multiple data streams. It introduces three extensions of one-dimensional betting-based CSs—a weighted Bonferroni region, a max‑wealth form, and a portfolio region—highlighting that the portfolio is tighter but computationally challenging. To make it practical, the authors propose tractable outer approximations (bounding box, π‑ellipsoid, and their intersection) that preserve validity and outperform existing methods in experiments, enabling applications such as multi‑metric A/B testing and model comparison.

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