Reliever: Relieving the Burden of Costly Model Fits for Changepoint Detection

TL;DR

Reliever is a method that reduces the computational cost of changepoint detection by minimizing model fits through proxy models, compatible with existing grid-search routines, and effective in high-dimensional settings.

Contribution

It introduces a novel approach that cuts the number of model fits directly, improving efficiency while maintaining accuracy in changepoint detection.

Findings

Reliever achieves rapid and accurate changepoint detection.

Coupled with optimal grid-search, it yields rate-optimal estimators up to a logarithmic factor.

Numerical experiments confirm its effectiveness across various models.

Abstract

Changepoint detection typically relies on a grid-search strategy for optimal data segmentation. When model fitting itself is expensive, repeatedly fitting a model on every candidate segment dominates the computation. Existing approaches mitigate this by pruning the grid, thus reducing the number of segments (and model fits). We propose Reliever, which instead cuts the number of model fits directly and nests seamlessly within standard grid-search routines. Reliever fits a small, deterministic collection of proxy models and reuses them wherever they apply, making it compatible with a wide range of existing algorithms. For high-dimensional regression with changepoints, coupling Reliever with an optimal grid-search method yields changepoint and coefficient estimators that are rate-optimal up to a logarithmic factor. Extensive numerical experiments demonstrate that Reliever rapidly and accurately detects changepoints across a wide range of high-dimensional and nonparametric models.