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The fused lasso, also known as (anisotropic) total variation denoising, is widely used for piecewise constant signal estimation with respect to a given undirected graph.
On the approximation of curves by line segments using dynamic programming
R. Bellman · 1961
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Nonlinear total variation based noise removal algorithms
L. Rudin, S. Osher, and E. Faterni · 1992
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Locally apadtive regression splines
E. Mammen and S. van de Geer · 1997
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Assouad, Fano, and Le Cam
B. Yu · 1997
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Minimax estimation via wavelet shrinkage
D. L. Donoho and I. M. Johnstone · 1998
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Fast approximate energy minimization via graph cuts
Y. Boykov, O. Veksler, and R. Zabih · 2001
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Introduction to Algorithms
T. Cormen, C. Stein, R. Rivest, and C. Leiserson · 2001
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Local extremes, runs, strings and multiresolution
P. L. Davies and A. Kovac · 2001
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Algebraic Graph Theory
C. Godsil and G. Royle · 2001
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Using manifold structure for partially labelled classification
M. Belkin and P. Niyogi · 2002
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Some remarks on distributed depth-first search
Y. H. Tsin · 2002
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Graph wavelets for spatial traffic analysis
M. Crovella and E. Kolaczyk · 2003
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Kernels and regularization on graphs
A. Smola and R. Kondor · 2003
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Semi-supervised learning using Gaussian fields and harmonic functions
X. Zhu, Z. Ghahramani, and J. Lafferty · 2003
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Sparsity and smoothness via the fused lasso
R. Tibshirani, M. Saunders, S. Rosset, J. Zhu, and K. Knight · 2005
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Learning from labeled and unlabeled data on a directed graph
D. Zhou, J. Huang, and B. Scholkopf · 2005
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Diffusion wavelets
R. Coifman and M. Maggioni · 2006
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Lower-stretch spanning trees
M. Elkin, Y. Emek, D. Spielman, and S.-H. Teng · 2008
Cited alongside, same era.
On total variation minimization and surface evolution using parametric maximum flows
A. Chambolle and J. Darbon · 2009
Cited alongside, same era.
Dynamic supernodes in sparse Cholesky update/downdate and triangular solves
T. Davis and W. Hager · 2009
Cited alongside, same era.
Community structure in large networks: Natural cluster sizes and the absence of large well-defined clusters
J. Leskovec, K. J. Lang, A. Dasgupta, and M. W. Mahoney · 2009
Cited alongside, same era.
Properties and refinements of the fused lasso
A. Rinaldo · 2009
Cited alongside, same era.
Introduction to Nonparametric Estimation
A. Tsybakov · 2009
Cited alongside, same era.
Using petal-decompositions to build a low stretch spanning tree
I. Abraham and O. Neiman · 2012
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A direct algorithm for 1d total variation denoising
L. Condat · 2012
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On pattern recovery of the fused lasso
J. Qian and J. Jia · 2012
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A dynamic programming algorithm for the fused lasso and l 0 l_{0} -segmentation
N. Johnson · 2013
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Detecting activations over graphs using spanning tree wavelet bases
J. Sharpnack, A. Krishnamurthy, and A. Singh · 2013
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The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains
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Multiscale wavelets on trees, graphs and high dimensional data: Theory and applications to semi supervised learning
M. Gavish, B. Nadler, and R. Coifman · 2010
Cited alongside, same era.
Multiple change-point estimation with a total variation penalty
Z. Harchaoui and C. Levy-Leduc · 2010
Cited alongside, same era.
A path algorithm for the fused lasso signal approximator
H. Hoefling · 2010
Cited alongside, same era.
Detecting weak but hierarchically-structured patterns in networks
A. Singh, R. Nowak, and R. Calderbank · 2010
Cited alongside, same era.
Distributed optimization and statistical learning via the alternating direction method of multipliers
S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein · 2011
Cited alongside, same era.
A first-order primal-dual algorithm for convex problems with applications to imaging
A. Chambolle and T. Pock · 2011
Cited alongside, same era.
D. Shuman, S. Narang, P. Frossard, A. Ortega, and P. Vandergheynst · 2013
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Modular proximal optimization for multidimensional total-variation regularization
Á. Barbero and S. Sra · 2014
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On the prediction performance of the lasso
A. Dalalyan, M. Hebiri, and J. Lederer · 2014
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On change point detection using the fused lasso method
C. R. Rojas and B. Wahlberg · 2014
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Adaptive piecewise polynomial estimation via trend filtering
R. J. Tibshirani · 2014
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Cut pursuit: fast algorithms to learn piecewise constant functions on general weighted graphs
L. Landrieu and G. Obozinski · 2015
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A fast and flexible algorithm for the graph-fused lasso
W. Tansey and J. Scott · 2015
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Optimal rates for total variation denoising
J.-C. Hutter and P. Rigollet · 2016
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Total variation on a tree
V. Kolmogorov, T. Pock, and M. Rolinek · 2016
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Approximate recovery in changepoint problems, from ℓ 2 \ell_{2} estimation error rates
K. Lin, J. Sharpnack, A. Rinaldo, and R. J. Tibshirani · 2016
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Total variation classes beyond 1d: Minimax rates, and the limitations of linear smoothers
V. Sadhanala, Y.-X. Wang, and R. J. Tibshirani · 2016
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Trend filtering on graphs
Y.-X. Wang, J. Sharpnack, A. Smola, and R. J. Tibshirani · 2016
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