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- W2634492528 abstract "We consider the problem of recovering a function input of a differential equation formulated on an unknown domain $M$. We assume to have access to a discrete domain $M_n={x_1, dots, x_n} subset M$, and to noisy measurements of the output solution at $ple n$ of those points. We introduce a graph-based Bayesian inverse problem, and show that the graph-posterior measures over functions in $M_n$ converge, in the large $n$ limit, to a posterior over functions in $M$ that solves a Bayesian inverse problem with known domain. The proofs rely on the variational formulation of the Bayesian update, and on a new topology for the study of convergence of measures over functions on point clouds to a measure over functions on the continuum. Our framework, techniques, and results may serve to lay the foundations of robust uncertainty quantification of graph-based tasks in machine learning. The ideas are presented in the concrete setting of recovering the initial condition of the heat equation on an unknown manifold." @default.
- W2634492528 created "2017-06-30" @default.
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- W2634492528 date "2017-06-22" @default.
- W2634492528 modified "2023-10-03" @default.
- W2634492528 title "Continuum Limit of Posteriors in Graph Bayesian Inverse Problems" @default.
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