We study the problems of sequential nonparametric two-sample and independence
testing. Sequential tests process data online and allow using observed data to
decide whether to stop and reject the null hypothesis or to collect more data
while maintaining type I error control. We build upon the principle of
(nonparametric) testing by betting, where a gambler places bets on future
observations and their wealth measures evidence against the null hypothesis.
While recently developed kernel-based betting strategies often work well on
simple distributions, selecting a suitable kernel for high-dimensional or
structured data, such as text and images, is often nontrivial. To address this
drawback, we design prediction-based betting strategies that rely on the
following fact: if a sequentially updated predictor starts to consistently
determine (a) which distribution an instance is drawn from, or (b) whether an
instance is drawn from the joint distribution or the product of the marginal
distributions (the latter produced by external randomization), it provides
evidence against the two-sample or independence nulls respectively. We
empirically demonstrate the superiority of our tests over kernel-based
approaches under structured settings. Our tests can be applied beyond the case
of independent and identically distributed data, remaining valid and powerful
even when the data distribution drifts over time.

本研究探讨了顺序非参数两样本和独立性检验的问题，提出了一种基于预测的赌博策略，用于解决高维结构化数据上核函数的选择问题。我们在实验中证明了这种方法优于基于核的方法，即使在数据分布随时间漂移的情况下，也仍然有效强大。