Uncertainty Quantification and Experimental Design for Large-Scale Linear Inverse Problems under Gaussian Process Priors. (arXiv:2109.03457v4 [stat.ML] UPDATED)

We consider the use of Gaussian process (GP) priors for solving inverse
problems in a Bayesian framework. As is well known, the computational
complexity of GPs scales cubically in the number of datapoints. We here show
that in the context of inverse problems involving integral operators, one faces
additional difficulties that hinder inversion on large grids. Furthermore, in
that context, covariance matrices can become too large to be stored. By
leveraging results about sequential disintegrations of Gaussian measures, we
are …

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