## Electronic Journal of Statistics

### Estimating a smooth function on a large graph by Bayesian Laplacian regularisation

#### Abstract

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.

#### Article information

Source
Electron. J. Statist. Volume 11, Number 1 (2017), 891-915.

Dates
First available in Project Euclid: 28 March 2017

https://projecteuclid.org/euclid.ejs/1490688317

Digital Object Identifier
doi:10.1214/17-EJS1253

#### Citation

Kirichenko, Alisa; van Zanten, Harry. Estimating a smooth function on a large graph by Bayesian Laplacian regularisation. Electron. J. Statist. 11 (2017), no. 1, 891--915. doi:10.1214/17-EJS1253. https://projecteuclid.org/euclid.ejs/1490688317

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