# An Efficient ADMM Algorithm for Structural Break Detection in Multivariate Time Series

arXiv: https://arxiv.org/abs/1711.08392 · HTML: https://mlsanity.com/paper/1711.08392/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Nov 2017.

## Built on by (most cited first, 1 of 1)

- [The non-overlapping statistical approximation to overlapping group lasso](https://mlsanity.com/paper/2211.09221/) (2022)

## Abstract (arXiv)

We present an efficient alternating direction method of multipliers (ADMM) algorithm for segmenting a multivariate non-stationary time series with structural breaks into stationary regions. We draw from recent work where the series is assumed to follow a vector autoregressive model within segments and a convex estimation procedure may be formulated using group fused lasso penalties. Our ADMM approach first splits the convex problem into a global quadratic program and a simple group lasso proximal update. We show that the global problem may be parallelized over rows of the time dependent transition matrices and furthermore that each subproblem may be rewritten in a form identical to the log-likelihood of a Gaussian state space model. Consequently, we develop a Kalman smoothing algorithm to solve the global update in time linear in the length of the series.