A0225
Title: Online correlation change detection for high-dimensional data
Authors: Jie Gao - Chinese university of Hong Kong(Shenzhen) (China) [presenting]
Liyan Xie - Georgia Institute of Technology (United States)
Zhaoyuan Li - The Chinese University of Hong Kong, Shenzhen (China)
Abstract: The problem of change point detection in the correlation structure of streaming high-dimensional data is explored, with minimum assumptions posed on the underlying data distribution and correlation structure. Depending on the /$L_1/$ and /$L_{\infty}/$ norm of squared difference of vectorized pre-change and post-change correlation matrices, dense and sparse settings are considered, respectively. Both window-limited and Shewhart-type test statistics are proposed. A novel method for threshold selection is designed based on sign-flip permutation. In addition, two enhancement techniques, synthetic minority oversampling technique (SMOTE) and knockoff, are combined with window-limited test statistics to tackle the instability in detection due to small sample sizes. Theoretical evaluations of these proposed methods are conducted regarding average run length and detection delay. Numerical studies are conducted to examine the finite sample performances of the proposed methods. The methods are effective in most simulation cases, as the average detection delays are very close to the exact CUSUM. Moreover, a combined /$L_1/$ and /$L_{\infty}/$ norm approach is applied and has expected performance for transitions from sparse to dense settings. Two real datasets, El Nino event prediction and seismic event, are also analyzed to illustrate the proposed methods' efficacy in detecting fundamental changes with minimal delay.
