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 the proposed method, combined with a novel topological feature embedding, performs well on both simulated and real image data.

翻译：我们提出一种适用于多变量变点检测的贝叶斯方法，该方法可同时推断变点位置和区分变点前后数据的逻辑回归模型系数。与多种多变量变点检测方法不同，本方法适用于混合类型数据，并避免对数据分布及变化性质施加严格假设。回归系数为潜在复杂变化提供可解释的描述。在贝叶斯后验推断中，该模型基于Pólya-gamma数据增广技术实现了简单的Gibbs采样算法。我们建立了保证方法能恢复真实潜在变点的充分条件。作为方法验证场景，我们考虑了图像序列中拓扑变化检测问题。实验表明，本方法与新型拓扑特征嵌入相结合，在模拟数据和真实图像数据上均表现良好。