We study distribution-free sequential changepoint detection for independent observations with unknown and unrestricted pre- and post-change laws. We build on the conformal test martingales and associated e-detectors of Vovk(2021), which control the probability of false alarm (PFA) and the average run length (ARL) respe...
Reinforcement learning and contextual bandit algorithms have become increasingly common in sequential decision-making applications. When these methods are deployed in high-stakes domains, there is growing interest not only in learning effective policies, but also in conducting statistical inference for quantities learn...
James Leiner, Aurélien F. Bibaut, Nathan Kallus et al.· 0 citations
We give a necessary and sufficient condition for the existence of power-one sequential tests in an i.i.d. composite testing problem. A level-\(\alpha\) test with power one against every alternative exists if and only if the alternatives are separated from the null by a countable family of finite-block events. We provid...
We study a minimal classification problem: Given independent labeled observations $X\sim P$ and $Z\sim Q$ from two unknown distributions $P,Q$, and given an independent target $Y$ drawn with equal probability from $P$ or $Q$, can one classify $Y$ strictly better than chance whenever $P\neq Q$? The one-nearest-neighbor...
Suppose we are given an ordered sequence of independent data whose distribution changes $K$ times at unknown locations, for some unknown $K \geq 0$. In this paper, we study the problem of performing distribution-free inference on $K$. First, we show an impossibility result: any distribution-free upper confidence bound...
Given $[0,1]$-valued random variables $X_1,\dots,X_n$ such that $\mathbb{E}[X_i | X_1,\dots,X_{i-1}]= \mu$ for all $i$, we propose a new nonasymptotic confidence interval for $\mu$ that is obtained by inverting terminal e-values generated by a novel betting strategy. When the data are iid, its limiting width matches th...
Diego Martinez-Taboada, Aaditya Ramdas· 1 citation
Given observations $\mathbf x=(x_1,\dots,x_n)$, Gaffke (2005) defined \[ K_n(\mathbf x)=\mathbb{P}_{\mathbf D}\!\left\{\sum_{i=1}^n x_iD_i\le 1\right\}, \qquad (D_0,D_1,\ldots,D_n)\sim\mathrm{Dirichlet}(1,\ldots,1), \] and conjectured that it is a $p$-value whenever the inputs are independent e-values. Recently, Vlassi...
Jiahao Ming, Aaditya Ramdas, Yi Shen et al.· arXiv.org· 4 citations· ⚡1
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