mlsanityData to 14 Oct 2026

Adaptive and non-adaptive minimax rates for weighted Laplacian-eigenmap based nonparametric regression

arXiv 2311.00140 ↗First posted 31 Oct 2023math.ST stat.ML stat.THcited by 5

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Abstract (arXiv)

We show both adaptive and non-adaptive minimax rates of convergence for a family of weighted Laplacian-Eigenmap based nonparametric regression methods, when the true regression function belongs to a Sobolev space and the sampling density is bounded from above and below. The adaptation methodology is based on extensions of Lepski's method and is over both the smoothness parameter (s∈mathbbN+) and the norm parameter (M>0) determining the constraints on the Sobolev space. Our results extend the non-adaptive result in citegreen2021minimax, established for a specific normalized graph Laplacian, to a wide class of weighted Laplacian matrices used in practice, including the unnormalized Laplacian and random walk Laplacian.

Key facts. Cited by 5 papers in the map (data through 14 Oct 2026). Builds on 14 of its 69 references that are in the map. First posted on arXiv 31 Oct 2023.

Builds on

14 of 69 references.

References · 14

  1. 2018The Laplacian in RL: Learning Representations with Efficient Approximationscited by 86
  2. 2018Error estimates for spectral convergence of the graph Laplacian on random geometric graphs towards the Laplace--Beltrami operatorcited by 70
  3. 2014Trend Filtering on Graphscited by 45
  4. 2015A variational approach to the consistency of spectral clusteringcited by 28
  5. 2018Large Data and Zero Noise Limits of Graph-Based Semi-Supervised Learning Algorithmscited by 22
  6. 2017On the Optimality of Kernel-Embedding Based Goodness-of-Fit Testscited by 19
  7. 2021Minimax Optimal Regression over Sobolev Spaces via Laplacian Regularization on Neighborhood Graphscited by 13
  8. 2019Spectral Analysis Of Weighted Laplacians Arising In Data Clusteringcited by 11
  9. 2019A maximum principle argument for the uniform convergence of graph Laplacian regressorscited by 9
  10. 2016A Spectral Series Approach to High-Dimensional Nonparametric Regressioncited by 8
  11. 2021Topologically penalized regression on manifoldscited by 5
  12. 2021Minimax Optimal Regression over Sobolev Spaces via Laplacian Eigenmaps on Neighborhood Graphscited by 5
2 more
  1. 2016Data driven estimation of Laplace-Beltrami operatorcited by 4
  2. 2022Rates of Convergence for Regression with the Graph Poly-Laplaciancited by 4

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 3; 2025: 1; 2026: 1.

5 papers.

  1. 2025On the Rate of Convergence of Kolmogorov-Arnold Network Regression Estimatorscited by 4
  2. 2024Nonsmooth Nonparametric Regression via Fractional Laplacian Eigenmapscited by 2
  3. 2024Nonparametric regression on random geometric graphs sampled from submanifoldscited by 1
  4. 2024Node Regression on Latent Position Random Graphs via Local Averagingcited by 0
  5. 2026Graph Memory: Spectral Associative Memory via Dirichlet Energycited by 0