文章基本信息

标题：Estimating a smooth function on a large graph by Bayesian Laplacian regularisation
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作者：Alisa Kirichenko ; Harry van Zanten
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2017
卷号：11
期号：1
页码：891-915
DOI：10.1214/17-EJS1253
语种：English
出版社：Institute of Mathematical Statistics
摘要：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.