Recent Advances in Change-Point Analysis with Applications to Modeling Complex Dependent Data

Multiple changepoint analyses have become an important tool in modern statistics. Classical approaches to the problem include dynamic programming, binary segmentation procedures and their variants, and windowed approaches. Fast dynamic programming procedures that optimize penalized likelihoods only apply when all model parameters change at each and every changepoint time, which is often physically unrealistic. Similarly, windowed approaches either assume that all dynamics change at each changepoint time, or that aspects that do not change at the changepoint time vary across windows. Penalized likelihood methods for the general case, where only a subset of parameters are allowed to change at the changepoint times, require extensive computational searches, classically done via genetic algorithms, to locate the optimal changepoint configuration.

This paper develops methods that rapidly estimate optimal penalized likelihood changepoint configurations in the general case, bypassing the slow computational (and stochastic) drawbacks of genetic algorithms. Consistency of the changepoint configuration and model parameters under infill asymptotics are proven; the procedure is shown to work well in finite samples via simulation. Applications to environmental and business problems are detailed.

Joint work with Colin Gallagher, Robert Lund, and Xueheng Shi. 

(Large-scale) streaming data are generated or encountered in many real-world applications ranging from biosurveillance and public/personal heath to environmental monitoring and network security to finance and economics and so on. Often one would like to utilize observed streaming data to make efficient sequential or quickest decision subject to the resources or sampling constraints in which the decision maker is responsible to actively choose partial data to be observed. In this talk, we present our latest research on active sequential change-point detection when monitoring high-dimensional streaming data, and apply multi-armed bandit (MAB) and federated learning to develop algorithms that are statistically efficient and computationally scalable under the sampling control. Asymptotic analysis, numerical studies, and their adaptions to case studies such as hot-spots detection of images or infectious diseases will be presented. 

In sequences comprising multivariate observations or non-Euclidean data objects such as networks, local dependencies often arise and can lead to inaccurate change-point detection. We propose a versatile framework that accommodates such sequences without imposing distributional assumptions on the observations, while being applicable to both high-dimensional and non-Euclidean data. This framework provides closed-form expressions for the test statistic and for approximating the p-value, allowing for efficient application in practice. Because it is often unclear whether a sequence exhibits local dependency in real applications, we further introduce a data-driven criterion to guide implementation of the proposed approach. 

In this talk, we propose an autoregressive tensor model, with time-dependent regression coefficients. With respect to the regression coefficients, three different regimes are considered: stationary, smooth-varying and abruptly-changing. We propose a computationally-efficient estimation procedure to handle these three regimes simultaneously, supported with theoretical guarantees and numerical experiments. Two extensions are considered: dynamic community detection in these three regimes and an estimation procedure for a more general class of time series models.