Modified path algorithm of fused Lasso signal approximator for consistent recovery of change points

• Published in: Journal of statistical planning and inference Vol. 200; pp. 223 - 238
• Main Authors: Son, Won, Lim, Johan
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.05.2019
• Subjects: Change points; Fused lasso signal approximator; Modified path algorithm; Total variation penalty; Modified path algorithm; Fused lasso signal approximator; Change points; 62J07; Total variation penalty; 62L10
• ISSN: 0378-3758; 1873-1171
• DOI: 10.1016/j.jspi.2018.10.003

The path algorithm of the fused lasso signal approximator is known to fail in finding change points when monotonically increasing or decreasing blocks exist in the mean vector. In this paper, we first understand why the standard path algorithm by Hoefling (2010) fails in the primal optimization problem. We then propose a modified path algorithm for the consistent recovery of the change points and study its properties theoretically and numerically. •The path algorithm for fused lasso signal approximator fails in finding change points when monotonic blocks exist in the mean vector.•We understand why the standard path algorithm in the literature fails in the primal optimization problem.•We propose a modified path algorithm for the consistent recovery of the change points.