A generalized Bayesian approach to multiple changepoint analysis

TL;DR

This paper presents a flexible Bayesian method for detecting multiple changepoints in data without assuming a specific data-generating process, using multinomial logistic regression for interpretability.

Contribution

It introduces a generalized Bayesian approach that combines changepoint detection with multinomial logistic regression, avoiding restrictive assumptions and enabling simultaneous inference.

Findings

Accurately detects changepoints across various data types

Provides interpretable coefficients for complex changes

Demonstrates effectiveness on financial and topological data

Abstract

We introduce a generalized Bayesian method for multiple changepoint analysis with a loss function inspired by multinomial logistic regression. The method does not require a specification of the data-generating process and avoids restrictive assumptions on the nature of changepoints. From the joint posterior distribution, we can make simultaneous inference on the locations of changepoints and the coefficients of a multinomial logistic regression model for distinguishing data across homogeneous segments. The multinomial logistic regression coefficients provide a familiar means of interpreting potentially complex changes. To select the number of changepoints, we leverage posterior summaries that measure whether the multinomial logistic classifier can distinguish data from either side of a potential changepoint. To simulate from the generalized posterior distribution, we present a Gibbs sampler based on P\'olya-Gamma data augmentation. We assess the accuracy and flexibility of our method through simulation studies featuring different types of changes and demonstrate its interpretability through applications to financial network data and topological data derived from nanoparticle videos.