变点数量的无分布推断
Distribution-free inference on the number of changepoints
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- Stanford University（斯坦福大学）
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中文总结 AI 辅助
本文针对未知变点数量的无分布推断问题，证明了上界不可行，并提出基于共形p值的有限样本有效下界方法CLOCC，具有普适性，在合成和真实数据实验中验证了其实用性。
中文摘要 AI 辅助
假设我们给定一个独立数据的有序序列，其分布在未知位置发生 $K$ 次变化，其中 $K \geq 0$ 未知。本文研究对 $K$ 进行无分布推断的问题。首先，我们展示一个不可能性结果：任何关于 $K$ 的无分布上置信界必然是平凡且无信息的。然后，利用共形 $p$ 值，并且仅在变点所划分的数据段（段内）可交换且（段间）相互独立的假设下，我们构造了 $K$ 的有限样本有效下置信界，称之为变点计数的共形下界（CLOCC）。我们证明，在所陈述的假设下，CLOCC 是提供 $K$ 下界的唯一可行方法，我们将此性质称为其普适性。我们提供了选择能产生高效且紧凑下界的得分函数的实用指南。我们在多个合成和真实数据实验中评估了 CLOCC，它在这些实验中提供了有信息量的 $K$ 下界，展示了其实用适用性。
英文摘要
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 on $K$ must be trivial and uninformative. Then, using conformal $p$-values, and under only the assumption that the data segments induced by the changepoints are exchangeable (within themselves) and mutually independent, we construct a finite-sample valid lower confidence bound on $K$, which we call the Conformal LOwer bound on Changepoint Count (CLOCC). We show that CLOCC is the only feasible way to provide a lower bound on $K$ under the stated assumptions, a property we refer to as its universality. We provide practical guidelines for choosing score functions that yield efficient and tight lower bounds. We evaluate CLOCC in several synthetic and real-data experiments, where it provides informative lower bounds on $K$, demonstrating its practical applicability.
