Testing Exchangeability With Martingale for Change-Point Detection

Abstract

This work proposes a new exchangeability test for a random sequence through a martingale-based approach. Its main contributions include 1) an additive martingale which is more amenable for designing exchangeability tests by exploiting the Hoeffding-Azuma lemma and 2) different betting functions for constructing the additive martingale. By choosing the underlying probability density function of p-values as a betting function, it can be shown that, when a change-point appears, a satisfying trade-off between the smoothness and expected one-step increment of the martingale sequence can be obtained. An online algorithm based on beta distribution parametrization for constructing this betting function is discussed in detail as well.