Despite relaxed assumptions, the proposed method possesses proven theoretical guarantees for both detection and localization.

Identifying change points (CPs) in a time series is crucial to guide better decision making across various fields like finance and healthcare and facilitating timely responses to potential risks or opportunities. Existing Change Point Detection (CPD) methods have a limitation in tracking changes in the joint distribution of multidimensional features. In addition, they fail to generalize effectively within the same time series as different types of CPs may require different detection methods. As the volume of multidimensional time series continues to grow, capturing various types of complex CPs such as changes in the correlation structure of the time-series features has become essential. To overcome the limitations of existing methods, we propose TiVaCPD, an approach that uses a Time-Varying Graphical Lasso (TVGL) to identify changes in correlation patterns between multidimensional features over time, and combines that with an aggregate Kernel Maximum Mean Discrepancy (MMD) test to identify changes in the underlying statistical distributions of dynamic time windows with varying length. The MMD and TVGL scores are combined using a novel ensemble method based on similarity measures leveraging the power of both statistical tests. We evaluate the performance of TiVaCPD in identifying and characterizing various types of CPs and show that our method outperforms current state-of-the-art methods in real-world CPD datasets. We further demonstrate that TiVaCPD scores characterize the type of CPs and facilitate interpretation of change dynamics, offering insights into real-life applications.

Bayesian change-point detection, together with latent variable models, allows to perform segmentation over high-dimensional time-series. We assume that change-points lie on a lower-dimensional manifold where we aim to infer subsets of discrete latent variables. For this model, full inference is computationally unfeasible and pseudo-observations based on point-estimates are used instead. However, if estimation is not certain enough, change-point detection gets affected. To circumvent this problem, we propose a multinomial sampling methodology that improves the detection rate and reduces the delay while keeping complexity stable and inference analytically tractable. Our experiments show results that outperform the baseline method and we also provide an example oriented to a human behavior study.

We introduce a novel geometry-oriented methodology, based on the emerging tools of topological data analysis, into the change point detection framework. The key rationale is that change points are likely to be associated with changes in geometry behind the data generating process. While the applications of topological data analysis to change point detection are potentially very broad, in this paper we primarily focus on integrating topological concepts with the existing nonparametric methods for change point detection. In particular, the proposed new geometry-oriented approach aims to enhance detection accuracy of distributional regime shift locations. Our simulation studies suggest that integration of topological data analysis with some existing algorithms for change point detection leads to consistently more accurate detection results. We illustrate our new methodology in application to the two closely related environmental time series datasets -ice phenology of the Lake Baikal and the North Atlantic Oscillation indices, in a research query for a possible association between their estimated regime shift locations.

Change-point detection (CPD) aims to locate abrupt transitions in the generative model of a sequence of observations. When Bayesian methods are considered, the standard practice is to infer the posterior distribution of the change-point locations. However, for complex models (high-dimensional or heterogeneous), it is not possible to perform reliable detection. To circumvent this problem, we propose to use a hierarchical model, which yields observations that belong to a lower-dimensional manifold. Concretely, we consider a latent-class model with an unbounded number of categories, which is based on the chinese-restaurant process (CRP). For this model we derive a continual learning mechanism that is based on the sequential construction of the CRP and the expectation-maximization (EM) algorithm with a stochastic maximization step. Our results show that the proposed method is able to recursively infer the number of underlying latent classes and perform CPD in a reliable manner.