
Graphbased approximation of Matérn Gaussian fields
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Graphbased approximation of Matérn Gaussian fields
Abstract: Matérn Gaussian fields (MGFs) have been popular modeling choices in many aspects of Bayesian methodologies. In this presentation we will discuss a generalization of MGFs to manifolds and graphs. In the first part, we formalize the definition of MGFs on manifolds by exploiting the stochastic partial differential equation representation of the usual MGFs on Euclidean domains. Sparse approximation based on a graph discretization is then introduced together with a convergence analysis. Numerical experiments will demonstrate their wide applicability. In the second part, we study a related graphbased Bayesian semisupervised learning problem using the framework developed so far. We show that optimal (up to logarithmic factors) posterior contraction rates can be achieved if sufficiently many unlabeled data are available, thereby demonstrating the benefits of unlabeled data in this specific setting.
Ruiyi is a fifthyear Ph.D. student in computational and applied mathematics at the University of Chicago, advised by Prof. Daniel SanzAlonso. He obtained a Bachelor's degree in Mathematics at UCLA. His research interests lie broadly in the mathematical foundations of data science, including Bayesian inverse problems, graphbased machine learning and nonparametric statistics.