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2018 On the total variation regularized estimator over a class of tree graphs
Francesco Ortelli, Sara van de Geer
Electron. J. Statist. 12(2): 4517-4570 (2018). DOI: 10.1214/18-EJS1519


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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Francesco Ortelli. Sara van de Geer. "On the total variation regularized estimator over a class of tree graphs." Electron. J. Statist. 12 (2) 4517 - 4570, 2018.


Received: 1 June 2018; Published: 2018
First available in Project Euclid: 19 December 2018

zbMATH: 07003250
MathSciNet: MR3892703
Digital Object Identifier: 10.1214/18-EJS1519

Keywords: branched path graph , compatibility constant , edge Lasso , Fused lasso , harmonic mean , Irrepresentable Condition , Lasso , Oracle inequality , path graph , Total variation regularization , tree


Vol.12 • No. 2 • 2018
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