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This is a Quantitative Study study.

October 8, 2025Open Access

Minimax Rates for the Estimation of Eigenpairs of Weighted Laplace-Beltrami Operators on Manifolds

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The statistical minimax rate for eigenpair approximation is n^{-2/(d+4)}, indicating sharp convergence in weighted Laplace-Beltrami operators.
This study expands graph-based learning literature by analyzing stronger norms and achieving uniform convergence over smooth distributions.
Eigenpairs of graph Laplacians provide manifold agnostic estimators with approximations that align closely with lower bounds under high connectivity.
These findings enhance unsupervised learning techniques by applying robust statistical insights to eigenpair estimation from random data.

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Implication

Analysis reveals minimax rates for eigenpair estimation in weighted Laplace-Beltrami operators, indicating significant advancements in graph-based learning.

Cite This Study

Trillos et al. (2025) studied this question.

synapsesocial.com/papers/68e6bc5f38ca8e474d549f8f https://doi.org/10.48550/arxiv.2506.00171

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Implication

Analysis reveals minimax rates for eigenpair estimation in weighted Laplace-Beltrami operators, indicating significant advancements in graph-based learning.

Minimax Rates for the Estimation of Eigenpairs of Weighted Laplace-Beltrami Operators on Manifolds

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Discussion

Implication

Cite This Study

Minimax Rates for the Estimation of Eigenpairs of Weighted Laplace-Beltrami Operators on Manifolds

Key Points

Discussion

Implication

Cite This Study

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