Chen, X. (STAT) – Changepoint Detection and Clustering Methods for Multivariate Time Series and Attributed Networks

Time series data with dependence arise across a wide range of scientific and engineering disciplines, often presenting challenging inferential problems related to structural change and clustering. This Ph.D. proposal addresses several related problems in statistical inference for multivariate and network-indexed time series. First, we develop a weighted multivariate $U$-statistic procedure for detecting a single changepoint in the mean of a multivariate stationary time series. The proposed framework accommodates short-range dependence, encompasses classical CUSUM and Wilcoxon tests as special cases, and admits a tractable limiting distribution after a pre-whitening transformation. Second, we study nodal clustering in graphs with dynamic attributes through a decoder-only latent space framework that integrates temporal dynamics and structural information via a graph-fused LASSO regularization. An extension of this framework, in which the neural network decoder is replaced by an autoregressive structure at each node, is also introduced. Lastly, a future research project is proposed on modeling and changepoint inference for Arctic sea ice coverage data, whose marginal distribution is doubly inflated with point masses at zero and one. A latent Gaussian process transformation approach is outlined that accommodates this exotic marginal structure while permitting temporal and spatial autocorrelation, trends, and seasonal dynamics. In tandem, these efforts aim to provide flexible and theoretically grounded tools for analyzing complex dependent data.

Event Host: Xi Chen, Ph.D. Student, Statistical Science

Advisor: Robert Lund

Zoom: https://ucsc.zoom.us/j/97760514185?pwd=ImfeI5uEdBvq9eoiFXnF5pecmwfVHd.1

Passcode: 333103