A0402
Title: Multiple change point detection in tensors
Authors: Jiaqi Huang - Beijing Normal University (China) [presenting]
Junhui Wang - Chinese University of Hong Kong (Hong Kong)
Lixing Zhu - Beijing Normal University (China)
Xuehu Zhu - Xi'an Jiaotong university (China)
Abstract: A criterion is proposed for detecting change structures in tensor data. To accommodate tensor structures that may have a structural mode that is not suitable to be summarized in a distance to measure the difference between any two adjacent tensors, a mode-based signal-screening Frobenius distance for the moving sums of slices of tensor data is defined to handle both dense and sparse model structures of the tensors. It can also deal with the case without structural mode as a general distance. Based on the distance, signal statistics are then constructed using the ratios with adaptive-to-change ridge functions. The number of changes and their locations can then be consistently estimated in certain senses, and the confidence intervals of the locations of change points are constructed. The results hold when the size of the tensor and the number of change points diverge at certain rates, respectively. Numerical studies are conducted to examine the finite sample performances of the proposed method. Two real data examples are also analyzed for illustration.
