The group fused Lasso for multiple change-point detection

TL;DR

This paper introduces the group fused Lasso method for detecting shared change-points across multiple signals, providing efficient algorithms and theoretical guarantees supported by empirical results.

Contribution

The paper proposes a novel group fused Lasso approach with fast algorithms and consistency conditions for multiple change-point detection in multivariate signals.

Findings

Algorithms are proven to be consistent as the number of signals grows.

Empirical results validate the method on simulated data.

Effective detection of shared change-points in genomic data.

Abstract

We present the group fused Lasso for detection of multiple change-points shared by a set of co-occurring one-dimensional signals. Change-points are detected by approximating the original signals with a constraint on the multidimensional total variation, leading to piecewise-constant approximations. Fast algorithms are proposed to solve the resulting optimization problems, either exactly or approximately. Conditions are given for consistency of both algorithms as the number of signals increases, and empirical evidence is provided to support the results on simulated and array comparative genomic hybridization data.