Rates of convergence for Laplacian semi-supervised learning with low labeling rates

DOI10.1007/s40687-022-00371-xOpenAlexW3034023082MaRDI QIDQ2683473

Matthew Thorpe, Dejan Slepčev, Jeff Calder

Publication date: 10 February 2023

Published in: Research in the Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2006.02765

zbMATH Keywords

asymptotic consistencygamma-convergenceregressionrandom walks on graphssemi-supervised learningnon-local variational problemsPDEs on graphs

Mathematics Subject Classification ID

Asymptotic properties of nonparametric inference (62G20) Applications of graph theory (05C90) Sums of independent random variables; random walks (60G50) Learning and adaptive systems in artificial intelligence (68T05) Graph theory (including graph drawing) in computer science (68R10) Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) (60J20) Variational methods for second-order elliptic equations (35J20) Random walks on graphs (05C81)

Related Items (2)

A compactness theorem for functions on Poisson point clouds ⋮ Poisson Reweighted Laplacian Uncertainty Sampling for Graph-Based Active Learning

Uses Software

• GraphLearning

Cites Work

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• Continuum limit of total variation on point clouds
• Semi-supervised learning on Riemannian manifolds
• A variational approach to the consistency of spectral clustering
• Large data and zero noise limits of graph-based semi-supervised learning algorithms
• Elliptic partial differential equations of second order
• Consistency of modularity clustering on random geometric graphs
• Weighted nonlocal Laplacian on interpolation from sparse data
• A transportation \(L^p\) distance for signal analysis
• Analysis and algorithms for \(\ell_p\)-based semi-supervised learning on graphs
• Improved spectral convergence rates for graph Laplacians on \(\varepsilon \)-graphs and \(k\)-NN graphs
• Error estimates for spectral convergence of the graph Laplacian on random geometric graphs toward the Laplace-Beltrami operator
• From graph to manifold Laplacian: the convergence rate
• Optimal Cheeger cuts and bisections of random geometric graphs
• Deep limits of residual neural networks
• Consistency of Cheeger and Ratio Graph Cuts
• Continuum Limits of Posteriors in Graph Bayesian Inverse Problems
• Random Walk: A Modern Introduction
• Random Geometric Graphs
• Consistency of Dirichlet Partitions
• The game theoreticp-Laplacian and semi-supervised learning with few labels
• Consistency of Lipschitz Learning with Infinite Unlabeled Data and Finite Labeled Data
• A Maximum Principle Argument for the Uniform Convergence of Graph Laplacian Regressors
• Large data limit for a phase transition model with the p-Laplacian on point clouds
• A continuum limit for the PageRank algorithm
• Mumford–Shah functionals on graphs and their asymptotics
• Analysis of $p$-Laplacian Regularization in Semisupervised Learning
• Estimating perimeter using graph cuts
• Concentration Inequalities for Sums and Martingales
• Asymptotic analysis of the Ginzburg–Landau functional on point clouds
• Learning Theory
• Optimal Transport for Manifold-Valued Images

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