Testing exchangeability with martingale for change-point detection

TL;DR

This paper introduces a novel martingale-based exchangeability test for change-point detection, leveraging additive martingales and betting functions to improve detection sensitivity and provide an online algorithm for practical implementation.

Contribution

It presents a new additive martingale approach for exchangeability testing, including a Beta distribution-based online algorithm for change-point detection.

Findings

Effective change-point detection when a distribution shift occurs.

The proposed martingale method balances smoothness and sensitivity.

Online algorithm demonstrates practical applicability.

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; 2) different betting functions for constructing the additive martingale are studied. 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.