Nonparametric Regression on Random Geometric Graphs Sampled from Submanifolds
Authors: Paul Rosa, Judith Rousseau
JMLR 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | We consider the nonparametric regression problem when the covariates are located on an unknown compact submanifold of a Euclidean space. Under deļ¬ning a random geometric graph structure over the covariates we analyse the asymptotic frequentist behaviour of the posterior distribution arising from Bayesian priors designed through random basis expansion in the graph Laplacian eigenbasis. Under H older smoothness assumption on the regression function and the density of the covariates over the submanifold, we prove that the posterior contraction rates of such methods are minimax optimal (up to logarithmic factors) for any positive smoothness index. |
| Researcher Affiliation | Academia | Paul Rosa EMAIL Department of Statistics University of Oxford 24-29 St Giles , Oxford OX1 3LB, United Kingdom; Judith Rousseau EMAIL Department of Statistics University of Oxford 24-29 St Giles , OX1 3LB Oxford, United Kingdom and CEREMADE, CNRS Universit e Paris-Dauphine, PSL University Place du Mar echal de Lattre de Tassigny, 75775 Paris Cedex 16, France |
| Pseudocode | No | The paper describes mathematical derivations, theorems, and proofs related to nonparametric regression and graph Laplacian eigenbasis. It does not include any clearly labeled pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not contain any explicit statements about releasing source code for the methodology described, nor does it provide links to any code repositories. It mentions a CC-BY 4.0 license for the paper itself but not for code. |
| Open Datasets | No | The paper is theoretical and focuses on mathematical properties of nonparametric regression models on submanifolds, rather than empirical evaluation with specific datasets. It discusses theoretical constructs like 'covariates xi RD' and 'manifold M' but does not refer to any concrete, publicly available datasets for experimental purposes. |
| Dataset Splits | No | The paper is theoretical and does not involve experiments on datasets, therefore, there are no dataset splits mentioned. |
| Hardware Specification | No | The paper focuses on theoretical contributions and does not describe any experimental setup that would require hardware specifications. |
| Software Dependencies | No | The paper focuses on theoretical contributions and does not describe any experimental setup that would require specific software dependencies with version numbers for reproducibility. |
| Experiment Setup | No | The paper is theoretical, presenting mathematical proofs and asymptotic behaviors of a statistical method. It does not contain an experimental setup with hyperparameters or training configurations. |