
Consistency of Bayesian inference with Gaussian process priors for a parabolic inverse problem
We consider the statistical nonlinear inverse problem of recovering the ...
read it

Allatonce formulation meets the Bayesian approach: A study of two prototypical linear inverse problems
In this work, the Bayesian approach to inverse problems is formulated in...
read it

Consistency of Bayesian inference with Gaussian process priors in an elliptic inverse problem
For O a bounded domain in R^d and a given smooth function g:O→R, we cons...
read it

Stabilities of Shape Identification Inverse Problems in a Bayesian Framework
A general shape identification inverse problem is studied in a Bayesian ...
read it

On Bayesian Consistency for Flows Observed Through a Passive Scalar
We consider the statistical inverse problem of estimating a background f...
read it

Sparse image reconstruction on the sphere: a general approach with uncertainty quantification
Inverse problems defined naturally on the sphere are becoming increasing...
read it

Bayesian variational regularization on the ball
We develop variational regularization methods which leverage sparsitypr...
read it
Continuum Limit of Posteriors in Graph Bayesian Inverse Problems
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, ..., x_n}⊂ M, and to noisy measurements of the output solution at p< n of those points. We introduce a graphbased Bayesian inverse problem, and show that the graphposterior 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 graphbased 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.
READ FULL TEXT
Comments
There are no comments yet.