How to monitor and mitigate stair-casing in L1 trend filtering

Cristian R. Rojas; Bo Wahlberg

ICASSP 2015accepted0 citations

How to monitor and mitigate stair-casing in L1 trend filtering

Abstract

In this paper we study the estimation of changing trends in time-series using ℓ 1 trend filtering. This method generalizes 1D Total Variation (TV) denoising for detection of step changes in means to detecting changes in trends, and it relies on a convex optimization problem for which there are very efficient numerical algorithms. It is known that TV denoising suffers from the so-called stair-case effect, which leads to detecting false change points. The objective of this paper is to show that ℓ 1 trend filtering also suffers from a certain stair-case problem. The analysis is based on an interpretation of the dual variables of the optimization problem in the method as integrated random walk. We discuss consistency conditions for ℓ 1 trend filtering, how to monitor their fulfillment, and how to modify the algorithm to avoid the stair-case false detection problem.

BibTeX

@inproceedings{icassp2015_howtomonitorandm,
  title = {How to monitor and mitigate stair-casing in L1 trend filtering},
  author = {Cristian R. Rojas and Bo Wahlberg},
  booktitle = {ICASSP 2015},
  year = {2015}
}