On the total variation regularized estimator over a class of tree graphs
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Author / Producer
Date
2018-12-19
Publication Type
Journal Article
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yes
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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.
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Publication status
published
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Book title
Journal / series
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)