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Bayesian imaging with deep generative priors

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DDE - The mathematical and statistical foundation of future data-driven engineering

This talk presents a new Bayesian analysis and computation methodology to perform inference in high-dimensional problems where the prior knowledge is available in the form of a dataset of training examples, which we consider to be a sample from the marginal distribution of the unknown quantity of interest. Following the manifold hypothesis, which states that high-dimensional physical quantities encountered in the real world often lie along a low-dimensional latent manifold inside the ambient space, we construct a prior distribution that is supported on a low-dimensional manifold which is encoded by a deep neural network. The manifold and the distribution supported on the manifold can then be learnt from the training data by using modern machine learning techniques for generative modelling. We study the resulting Bayesian models theoretically and empirically by using a range of challenging imaging inverse problems and where we perform analyses related to uncertainty quantification, hypothesis testing, and model selection in the absence of ground truth.

This talk is part of the Isaac Newton Institute Seminar Series series.

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