We present a Bayesian method for multivariate changepoint detection that allows for simultaneous inference on the location of a changepoint and the coefficients of a logistic regression model for distinguishing pre-changepoint data from post-changepoint data. In contrast to many methods for multivariate changepoint detection, the proposed method is applicable to data of mixed type and avoids strict assumptions regarding the distribution of the data and the nature of the change. The regression coefficients provide an interpretable description of a potentially complex change. For posterior inference, the model admits a simple Gibbs sampling algorithm based on P\'olya-gamma data augmentation. We establish conditions under which the proposed method is guaranteed to recover the true underlying changepoint. As a testing ground for our method, we consider the problem of detecting topological changes in time series of images. We demonstrate that our proposed method $\mathtt{bclr}$, combined with a topological feature embedding, performs well on both simulated and real image data. The method also successfully recovers the location and nature of changes in more traditional changepoint tasks.

翻译：本文提出一种多元变点检测的贝叶斯方法，可同步推断变点位置以及用于区分变点前后数据的逻辑回归模型系数。与多数多元变点检测方法不同，本方法适用于混合类型数据，且无需对数据分布与变化性质作严格假设。回归系数为潜在复杂变化提供了可解释的描述框架。在后验推断方面，该模型通过Pólya-gamma数据增强实现了简洁的吉布斯采样算法。我们建立了该方法能够准确识别真实变点的理论条件。为验证方法有效性，我们以图像时间序列的拓扑结构变化检测作为测试场景。实验表明，本文提出的$\mathtt{bclr}$方法结合拓扑特征嵌入技术，在模拟与真实图像数据上均表现优异。该方法在传统变点检测任务中亦能准确识别变化位置与性质。