Almost all dynamic and random processes in nature go through sudden and significant structural changes. Often the change is in the observable quantity, e.g. fuel prices or stock indices or crime activities changing significantly in response to a change in an unobservable, latent factor such as an economic phenomenon or a public policy change, or a disease outbreak. Such ‘change-points’ are routinely observed across all scientific disciplines and applications, such as economics, epidemiology, social sciences, cybersecurity and finance. Specific examples could be changing regression when the observed variable depends on predictors through a mean structure that changes with time, or change points in data with massive dimensions, such as high-resolution imaging data or complex connected graphs. While there is a substantial literature proposing elaborate methods for detecting change points in different settings, there has been limited consideration of Bayesian methods for change-points in hierarchical models with complex dependence or sparsity structures. This research fills this gap with new statistical tools motivated by specific real-life applications, by developing theoretical framework while retaining efficiency and usefulness in current applications. The project integrates graduate education and training with statistical research, and emphasizes upholding societal and ethical considerations that create and foster an inclusive and diverse community.
In higher dimensions, the problem of detecting change-points and the changing structure is often rendered extremely difficult owing to a combinatorial computational complexity. Through this research, the PIs outline a comprehensive framework, both theoretical and methodological, in the context of change point estimation encompassing problems that may arise in different field of applications. In particular, the PIs build fundamentally new Bayesian methods that can 1) perform sparse signal recovery in a changing linear regression with consistency guarantees 2) detect change-points in dependence structure via changes in a Gaussian graphical model, and 3) build an innovative method for handling ‘ultra-high’-dimensional objects via random projections to drastically reduce the computational burden. Theoretical machinery will be developed to provide probabilistic rigor and consistency guarantee. Computationally efficient algorithms will be developed, and user-friendly software tools will be deployed in R for the usage of the developed methods by the scientific community at large.
This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
