A1173
Title: Higher-criticism for sparse multi-stream change-point detection
Authors: Tingnan Gong - Georgia Institute of Technology (United States) [presenting]
Alon Kipnis - Reichman University (Israel)
Yao Xie - Georgia Institute of Technology (United States)
Abstract: The focus is on a statistical procedure based on higher criticism (HC) to address the sparse multi-stream quickest change-point detection problem. Namely, the aim is to detect a potential change in the distribution of multiple data streams at some unknown time. If a change occurs, only a few streams are affected, whereas the identity of the affected streams is unknown. The HC-based procedure involves testing for a change point in individual streams and combining multiple tests using higher criticism. Relying on HC thresholding, the procedure also indicates a set of streams suspected to be affected by the change. A theoretical analysis is provided under a sparse heteroscedastic normal change-point model. An information-theoretic detection delay is established to lower bound when individual tests are based on the likelihood ratio or the generalized likelihood ratio statistics, and it is shown that the delay of the HC-based method converges in distribution to this bound. In the special case of constant variance, the bound coincides with the known results of a past study. It demonstrates the effectiveness of the HC-based method compared to other methods in detecting sparse changes through extensive numerical evaluations.
