Seeded Binary Segmentation: A general methodology for fast and optimal change point detection

TL;DR

Seeded binary segmentation is a versatile and efficient change point detection method that constructs background intervals for fast, near-linear time analysis, applicable to univariate, multivariate, and high-dimensional data, with proven optimality.

Contribution

The paper introduces seeded binary segmentation, a flexible, fast, and asymptotically minimax optimal approach for change point detection across various data dimensions.

Findings

Achieves near-linear computational complexity for univariate Gaussian mean changes.

Demonstrates asymptotic minimax optimality with appropriate selection methods.

Provides substantial computational gains in high-dimensional inverse covariance change detection.

Abstract

In recent years, there has been an increasing demand on efficient algorithms for large scale change point detection problems. To this end, we propose seeded binary segmentation, an approach relying on a deterministic construction of background intervals, called seeded intervals, in which single change points are searched. The final selection of change points based on the candidates from seeded intervals can be done in various ways, adapted to the problem at hand. Thus, seeded binary segmentation is easy to adapt to a wide range of change point detection problems, let that be univariate, multivariate or even high-dimensional. We consider the univariate Gaussian change in mean setup in detail. For this specific case we show that seeded binary segmentation leads to a near-linear time approach (i.e. linear up to a logarithmic factor) independent of the underlying number of change points. Furthermore, using appropriate selection methods, the methodology is shown to be asymptotically minimax optimal. While computationally more efficient, the finite sample estimation performance remains competitive compared to state of the art procedures. Moreover, we illustrate the methodology for high-dimensional settings with an inverse covariance change point detection problem where our proposal leads to massive computational gains while still exhibiting good statistical performance.