Changepoint localization is the problem of estimating the index at which a change occurred in the data generating distribution of an ordered list of data, or declaring that no change occurred. We present the broadly applicable MCP algorithm, which uses a matrix of conformal p-values to produce a confidence interval for a (single) changepoint under the mild assumption that the pre-change and post-change distributions are each exchangeable. We prove a novel conformal Neyman-Pearson lemma, motivating practical classifier-based choices for our conformal score function. Finally, we exemplify the MCP algorithm on a variety of synthetic and real-world datasets, including using black-box pre-trained classifiers to detect changes in sequences of images, text, and accelerometer data.

翻译：变点定位问题旨在估计有序数据列表中数据生成分布发生变化的位置索引，或判定未发生任何变化。本文提出具有广泛适用性的MCP算法，该算法利用保形p值矩阵，在仅需满足变化前与变化后分布各自可交换的温和假设下，为（单一）变点生成置信区间。我们证明了一个新颖的保形奈曼-皮尔逊引理，为基于分类器的保形评分函数选择提供了理论依据。最后，我们在多种合成与真实数据集上验证MCP算法的有效性，包括使用黑盒预训练分类器检测图像序列、文本序列及加速度计数据中的分布变化。