On the Complexity of the Weighted Fused Lasso

被引：8

作者：

Bento, Jose ^{[1
]}

Furmaniak, Ralph ^{[2
]}

Ray, Surjyendu ^{[1
]}

机构：

[1] Boston Coll, Chestnut Hill, MA 02467 USA

[2] Quant, Chestnut Hill, MA USA

来源：

IEEE SIGNAL PROCESSING LETTERS | 2018年 / 25卷 / 10期

关键词：

Filter; lasso; projection; proximal operator; sum of absolute differences; total variation; weights; ALGORITHMS;

D O I：

10.1109/LSP.2018.2867800

中图分类号：

TM [电工技术]; TN [电子技术、通信技术];

学科分类号：

0808 ; 0809 ;

摘要：

The solution path of the one-dimensional fused lasso for an n-dimensional input is piecewise linear with at most O(n) segments. However, existing proofs of this bound do not hold for the weighted fused lasso. At the same time, results for the generalized lasso, of which the weighted fused lasso is a special case, allow more than Omega(3(n)) segments. In this letter, we prove that the number of segments in the solution path of the weighted fused lasso is O(n(2)), and that, for some instances, it is Omega(n(2)). We also give a new, very simple, proof of the O(n) bound for the fused lasso.

引用

页码：1595 / 1599

页数：5

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