Change Point Detection in Tensor Data

This research focuses on the development of new statistical methods for detecting structural changes - known as change points - in high-dimensional tensor-valued time series data. Change point detection is a fundamental problem in statistics with broad applications in fields such as finance, neuroscience, climate science, and biomedical imaging, where complex data are often structured as tensors (multi-dimensional arrays).

Building on recent advances in vector and matrix factor models, the project aims to generalise existing change point detection methods to the tensor setting. Specifically, the research investigates how latent low-rank tensor structures evolve over time, and proposes novel algorithms that can efficiently detect multiple changes in such structures, even when they are subtle or closely spaced. The methodology combines dimension reduction via tensor factorisation with high-resolution detection strategies based on local covariance contrasts.

Key objectives include: developing robust estimators for latent components under piecewise stationary assumptions; designing efficient segmentation procedures for identifying change points; and providing theoretical guarantees for the accuracy and consistency of the proposed methods. The work also explores the trade-off between statistical power and computational efficiency in high-dimensional settings.

The resulting tools will be validated on both simulated and real-world data, with potential impact in areas where understanding evolving multi-way dependencies is crucial. This includes monitoring systemic risk in financial markets, detecting brain state transitions in neuroimaging, and identifying climate regime shifts in environmental data.