A1237
Title: Offline and online robust change point detection with heavy-tailed data
Authors: Yudong Chen - University of Warwick (United Kingdom) [presenting]
Yi Yu - University of Warwick (United Kingdom)
Mengchu Li - University of Birmingham (United Kingdom)
Tengyao Wang - London School of Economics (United Kingdom)
Edwin Tang - University of Warwick (United Kingdom)
Abstract: An offline mean change point testing problem is studied for high-dimensional data with exponentially or polynomially decaying tails. In each case, depending on the L0-norm of the mean change vector, dense and sparse regimes are separately considered. The boundary is characterized between the dense and sparse regimes under the above two tail conditions for the first time in the change point literature, and novel testing procedures are proposed that attain optimal rates in each of the four regimes up to a poly-iterated logarithmic factor. By comparing with previous results under Gaussian assumptions, the results quantify the costs of heavy-tailedness on the fundamental difficulty of change point testing problems for high-dimensional data. Sequential (online) change point detection with heavy-tailed observations is also studied. A procedure based on the median-of-means technique that controls the probability of false alarms while minimizing, in a minimax sense, the detection delay is proposed. The focus is on the high-dimensional version of this robust online detection problem.
