mlsanityData to 7 Oct 2026

Trend Filtering on Graphs

arXiv 1410.7690 ↗First posted 28 Oct 2014stat.ML cs.AI cs.LGcited by 45

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Abstract (arXiv)

We introduce a family of adaptive estimators on graphs, based on penalizing the ℓ1 norm of discrete graph differences. This generalizes the idea of trend filtering [Kim et al. (2009), Tibshirani (2014)], used for univariate nonparametric regression, to graphs. Analogous to the univariate case, graph trend filtering exhibits a level of local adaptivity unmatched by the usual ℓ2-based graph smoothers. It is also defined by a convex minimization problem that is readily solved (e.g., by fast ADMM or Newton algorithms). We demonstrate the merits of graph trend filtering through examples and theory.

Key facts. Cited by 45 papers in the map (data through 7 Oct 2026). First posted on arXiv 28 Oct 2014.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 15; 2022: 14; 2023: 7; 2024: 3; 2025: 4; 2026: 2.

45 papers.

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  1. 2021Elastic Graph Neural Networkscited by 67
  2. 2022A Survey on Graph Representation Learning Methodscited by 66
  3. 2021Graph Trend Filtering Networks for Recommendationscited by 53
  4. 2022Graph Filters for Signal Processing and Machine Learning on Graphscited by 53
  5. 2021Optimal Dynamic Regret in Exp-Concave Online Learningcited by 39
  6. 2022Optimal Dynamic Regret in Proper Online Learning with Strongly Convex Losses and Beyondcited by 27
  7. 2021Untrained Graph Neural Networks for Denoisingcited by 15
  8. 2023Towards Data-centric Graph Machine Learning: Review and Outlookcited by 15
  9. 2021Minimax Optimal Regression over Sobolev Spaces via Laplacian Regularization on Neighborhood Graphscited by 13
  10. 2023Online Label Shift: Optimal Dynamic Regret meets Practical Algorithmscited by 11
  11. 2021An Optimal Reduction of TV-Denoising to Adaptive Online Learningcited by 9
  12. 2021Graph Denoising with Framelet Regularizercited by 8
33 more
  1. 2022Second Order Path Variationals in Non-Stationary Online Learningcited by 7
  2. 2022Total Variation Graph Neural Networkscited by 7
  3. 2021Topologically penalized regression on manifoldscited by 5
  4. 2021Minimax Optimal Regression over Sobolev Spaces via Laplacian Eigenmaps on Neighborhood Graphscited by 5
  5. 2022Robust Time Series Dissimilarity Measure for Outlier Detection and Periodicity Detectioncited by 5
  6. 2023Adaptive and non-adaptive minimax rates for weighted Laplacian-eigenmap based nonparametric regressioncited by 5
  7. 2021Multivariate Trend Filtering for Lattice Datacited by 4
  8. 2021Tree-based Node Aggregation in Sparse Graphical Modelscited by 3
  9. 2021On Convex Clustering Solutionscited by 3
  10. 2022The Voronoigram: Minimax Estimation of Bounded Variation Functions From Scattered Datacited by 3
  11. 2022Towards Understanding Graph Neural Networks: An Algorithm Unrolling Perspectivecited by 2
  12. 2022Variance estimation in graphs with the fused lassocited by 2
  13. 2022Heterogeneous Federated Learning on a Graphcited by 2
  14. 2023Bayes optimal learning in high-dimensional linear regression with network side informationcited by 2
  15. 2024Nonsmooth Nonparametric Regression via Fractional Laplacian Eigenmapscited by 2
  16. 2021T-LoHo: A Bayesian Regularization Model for Structured Sparsity and Smoothness on Graphscited by 1
  17. 2022A Cross Validation Framework for Signal Denoising with Applications to Trend Filtering, Dyadic CART and Beyondcited by 1
  18. 2022Optimizing Diffusion Rate and Label Reliability in a Graph-Based Semi-supervised Classifiercited by 1
  19. 2022ASGNN: Graph Neural Networks with Adaptive Structurecited by 1
  20. 2023Inhomogeneous graph trend filtering via a l2,0 cardinality penaltycited by 1
  21. 2025Adaptive Estimation and Learning under Temporal Distribution Shiftcited by 1
  22. 2021Modelling Heterogeneity Using Bayesian Structured Sparsitycited by 0
  23. 2021DPC: Unsupervised Deep Point Correspondence via Cross and Self Constructioncited by 0
  24. 2022Large Graph Signal Denoising with Application to Differential Privacycited by 0
  25. 2023Skeleton Regression: A Graph-Based Approach to Estimation with Manifold Structurecited by 0
  26. 2023Stability and Generalization of lp-Regularized Stochastic Learning for GCNcited by 0
  27. 2024Understanding the Effect of GCN Convolutions in Regression Taskscited by 0
  28. 2024Node Regression on Latent Position Random Graphs via Local Averagingcited by 0
  29. 2025Risk Bounds For Distributional Regressioncited by 0
  30. 2025Joint estimation of smooth graph signals from partial linear measurementscited by 0
  31. 2025A Simple Method for PMF Estimation on Large Supportscited by 0
  32. 2026Gauge-Invariant, Parameter-Insensitive Regularization for Potential Recovery from Flow on Directed Graphscited by 0
  33. 2026Graph-dependent shrinkage priors for Bayesian trend filteringcited by 0