Change-Point Detection for Graphical Models in the Presence of Missing Values

Abstract

We propose estimation methods for change points in high-dimensional covariance structures with an emphasis on challenging scenarios with missing values. We advocate three imputation like methods and investigate their implications on common losses used for change-point detection. We also discuss how model selection methods have to be adapted to the setting of incomplete data. The methods are compared in a simulation study and applied to a time series from an environmental monitoring system. An implementation of our proposals within the R-package hdcd is available via the online supplementary materials.

Keywords:

• Covariance estimation
• Graphical Lasso
• High-dimensional models
• Incomplete data
• Precision matrix
• Time-varying models

Supplementary Materials

R-package hdcd:The R-package hdcd for high-dimensional change point detection available at https://github.com/mlondschien/hdcd implements our methods to find change points in GGMs with possibly missing values. README files explain the usage via some examples and describe how to reproduce the above mentioned simulation results and figures. Additionally, the hdcd R-package also implements some ongoing work on multivariate nonparametric change-point detection (see Kovács, Londschien, and Bühlmann 2021a). We plan to update the package to use a faster Graphical Lasso implementation and more flexible Graphical Elastic Net (see Kovács et al. 2012b) and eventually upload also to CRAN.

Acknowledgments

We thank an associate editor and two anonymous reviewers for constructive comments. Furthermore, we thank Tamás Garamhegyi, József Kovács (Department of Geology, Eötvös Loránd University, Budapest, Hungary), and József Szalai (General Directorate of Water Management, Budapest, Hungary) for the groundwater dataset and for providing hydrogeological interpretation of the found change points.

Additional information

Funding

Solt Kovács and Peter Bühlmann have received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 Research and Innovation Programme (grant agreement no. 786461 CausalStats—ERC-2017-ADG).