A linear time algorithm for multiscale quantile simulation

TL;DR

This paper introduces a linear time algorithm for multiscale quantile simulation that efficiently detects change-points in various regression models, significantly reducing computation time compared to existing quadratic methods.

Contribution

The authors develop an $ ext{O}(n)$ algorithm leveraging quasiconvexity, applicable to all exponential family regression models with convex penalties, improving scalability for large datasets.

Findings

Algorithm runs in linear time, significantly faster than previous methods.

Simulation results confirm high accuracy and efficiency.

Implementation available in R-package 'linearQ' on CRAN.

Abstract

Change-point problems have appeared in a great many applications for example cancer genetics, econometrics and climate change. Modern multiscale type segmentation methods are considered to be a statistically efficient approach for multiple change-point detection, which minimize the number of change-points under a multiscale side-constraint. The constraint threshold plays a critical role in balancing the data-fit and model complexity. However, the computation time of such a threshold is quadratic in terms of sample size $n$, making it impractical for large scale problems. In this paper we proposed an $\mathcal{O}(n)$ algorithm by utilizing the hidden quasiconvexity structure of the problem. It applies to all regression models in exponential family with arbitrary convex scale penalties. Simulations verify its computational efficiency and accuracy. An implementation is provided in R-package "linearQ" on CRAN.