Testing Exchangeability With Martingale for Change-Point Detection

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