In the analysis of sequential data, the detection of abrupt changes is
important in predicting future changes. In this paper, we propose statistical
hypothesis tests for detecting covariance structure changes in locally smooth
time series modeled by Gaussian Processes (GPs). We provide theoretically
justified thresholds for the tests, and use them to improve Bayesian Online
Change Point Detection (BOCPD) by confirming statistically significant changes
and non-changes. Our Confirmatory BOCPD (CBOCPD) algorithm finds multiple
structural breaks in GPs even when hyperparameters are not tuned precisely. We
also provide conditions under which CBOCPD provides the lower prediction error
compared to BOCPD. Experimental results on synthetic and real-world datasets
show that our new tests correctly detect changes in the covariance structure in
GPs. The proposed algorithm also outperforms existing methods for the
prediction of nonstationarity in terms of both regression error and log
likelihood.

文章提出了一种用于检测局部平滑时间序列的协方差结构变化的统计假设检验方法，称为 Confirmatory BOCPD (CBOCPD)，该方法通过确认统计显著性的变化和非变化来改善 Bayesian Online Change Point Detection (BOCPD) 算法，实验结果表明该算法产生了比现有方法更低的预测误差和更高的对数似然性。