Non-segmental Bayesian Detection of Multiple Change-points

TL;DR

The paper introduces NOSE, a Bayesian method for detecting multiple change-points by assessing posterior jump heights, offering consistent and accurate detection of various structural changes in data.

Contribution

It presents a novel non-segmental Bayesian approach that models change-points globally using a Gamma-Indian buffet process prior, ensuring consistency and minimax optimality.

Findings

NOSE accurately detects change-points in simulations.

It outperforms existing methods in real-world data examples.

The approach is effective for various types of structural changes.

Abstract

We propose an original and general NOn-SEgmental (NOSE) approach for the detection of multiple change-points. NOSE identifies change-points by the non-negligibility of posterior estimates of the jump heights. Alternatively, under the Bayesian paradigm, NOSE treats the step-wise signal as a global infinite dimensional parameter drawn from a proposed process of atomic representation, where the random jump heights determine the locations and the number of change-points simultaneously. The random jump heights are further modeled by a Gamma-Indian buffet process shrinkage prior under the form of discrete spike-and-slab. The induced maximum a posteriori estimates of the jump heights are consistent and enjoy zerodiminishing false negative rate in discrimination under a 3-sigma rule. The success of NOSE is guaranteed by the posterior inferential results such as the minimaxity of posterior contraction rate, and posterior consistency of both locations and the number of abrupt changes. NOSE is applicable and effective to detect scale shifts, mean shifts, and structural changes in regression coefficients under linear or autoregression models. Comprehensive simulations and several real-world examples demonstrate the superiority of NOSE in detecting abrupt changes under various data settings.