Online detection of continuous changes in stochastic processes

Abstract

We are concerned with detecting continuous changes in stochastic processes. In conventional studies on non-stationary stochastic processes, it is often assumed that changes occur abruptly. By contrast, we assume that they take place continuously. The proposed scheme consists of an efficient algorithm and rigorous theoretical analysis under the assumption of continuity. The contribution of this paper is as follows: We first propose a novel characterization of processes for continuous changes. We also present a time- and space-efficient online estimator of the characteristics. Then, employing the proposed estimate, we propose a method for detecting changes together with a criterion for tuning its hyper-parameter. Finally, the proposed methods are shown to be effective through experimentation involving real-life data from markets, servers, and industrial machines.