On the total variation regularized estimator over a class of tree graphs


Date

2018-12-19

Publication Type

Journal Article

ETH Bibliography

yes

Citations

Altmetric

Data

Abstract

We generalize to tree graphs obtained by connecting path graphs an oracle result obtained for the Fused Lasso over the path graph. Moreover we show that it is possible to substitute in the oracle inequality the minimum of the distances between jumps by their harmonic mean. In doing so we prove a lower bound on the compatibility constant for the total variation penalty. Our analysis leverages insights obtained for the path graph with one branch to understand the case of more general tree graphs. As a side result, we get insights into the irrepresentable condition for such tree graphs.

Publication status

published

Editor

Book title

Volume

12 (2)

Pages / Article No.

4517 - 4570

Publisher

Cornell University

Event

Edition / version

Methods

Software

Geographic location

Date collected

Date created

Subject

Total variation regularization; Lasso; Fused Lasso; Edge Lasso; Path graph; Branched path graph; Tree; Compatibility constants; Oracle inequality; Irrepresentable condition; Harmonic mean

Organisational unit

03717 - van de Geer, Sara (emeritus) / van de Geer, Sara (emeritus) check_circle

Notes

Funding

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