Online Kernel CUSUM for Change-Point Detection

11/28/2022
by   Song Wei, et al.
0

We develop an online kernel Cumulative Sum (CUSUM) procedure, which consists of a parallel set of kernel statistics with different window sizes to account for the unknown change-point location. Compared with many existing sliding window-based kernel change-point detection procedures, which correspond to the Shewhart chart-type procedure, the proposed procedure is more sensitive to small changes. We further present a recursive computation of detection statistics, which is crucial for online procedures to achieve a constant computational and memory complexity, such that we do not need to calculate and remember the entire Gram matrix, which can be a computational bottleneck otherwise. We obtain precise analytic approximations of the two fundamental performance metrics, the Average Run Length (ARL) and Expected Detection Delay (EDD). Furthermore, we establish the optimal window size on the order of log ( ARL) such that there is nearly no power loss compared with an oracle procedure, which is analogous to the classic result for window-limited Generalized Likelihood Ratio (GLR) procedure. We present extensive numerical experiments to validate our theoretical results and the competitive performance of the proposed method.

READ FULL TEXT
research
10/26/2022

Optimal Sub-sampling to Boost Power of Kernel Sequential Change-point Detection

We present a novel scheme to boost detection power for kernel maximum me...
research
05/25/2015

Sketching for Sequential Change-Point Detection

We study sequential change-point detection using sketches (linear projec...
research
07/05/2015

Scan B-Statistic for Kernel Change-Point Detection

Detecting the emergence of an abrupt change-point is a classic problem i...
research
09/01/2015

Multi-Sensor Slope Change Detection

We develop a mixture procedure for multi-sensor systems to monitor data ...
research
06/14/2022

Window-Limited CUSUM for Sequential Change Detection

We study the parametric online changepoint detection problem, where the ...
research
11/09/2018

Sequential Subspace Changepoint Detection

We consider the sequential changepoint detection problem of detecting ch...
research
10/15/2021

Fast Online Changepoint Detection via Functional Pruning CUSUM statistics

Many modern applications of online changepoint detection require the abi...

Please sign up or login with your details

Forgot password? Click here to reset