Open Access
2017 Estimating a smooth function on a large graph by Bayesian Laplacian regularisation
Alisa Kirichenko, Harry van Zanten
Electron. J. Statist. 11(1): 891-915 (2017). DOI: 10.1214/17-EJS1253


We study a Bayesian approach to estimating a smooth function in the context of regression or classification problems on large graphs. We derive theoretical results that show how asymptotically optimal Bayesian regularisation can be achieved under an asymptotic shape assumption on the underlying graph and a smoothness condition on the target function, both formulated in terms of the graph Laplacian. The priors we study are randomly scaled Gaussians with precision operators involving the Laplacian of the graph.


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Alisa Kirichenko. Harry van Zanten. "Estimating a smooth function on a large graph by Bayesian Laplacian regularisation." Electron. J. Statist. 11 (1) 891 - 915, 2017.


Received: 1 December 2016; Published: 2017
First available in Project Euclid: 28 March 2017

zbMATH: 1362.62112
MathSciNet: MR3629018
Digital Object Identifier: 10.1214/17-EJS1253

Primary: 62C10 , 62G20

Keywords: Function estimation on graphs , Laplacian regularisation , nonparametric Bayes

Vol.11 • No. 1 • 2017
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