Testing exchangeability with martingale for change-point detection

10/06/2018

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by   Liang Dai, et al.

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This work studies the exchangeability test for a random sequence through a martingale based approach. Its main contributions include: 1) an additive martingale is introduced, 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 betting function, it can be shown that, when 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 as well.