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Projected variational inference for high-dimensional Bayesian inverse problems

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DDEW03 - Computational Challenges and Emerging Tools

In this talk, I will present a class of transport-based projected variational inference methods to tackle the computational challenges of the curse of dimensionality and unaffordable evaluation cost for high-dimensional Bayesian inverse problems governed by complex models. We project the high-dimensional parameters to intrinsically low-dimensional data-informed subspaces and employ transport-based variational methods (Stein and Wasserstein variational gradient descent using kernels and neural networks) to push samples drawn from the prior to a projected posterior. Moreover, we employ fast surrogate models to approximate the parameter-to-observable map. I will present error bounds for the projected posterior distribution measured in Kullback—Leibler divergence. Numerical experiments will be presented to demonstrate the properties of our methods, including improved accuracy, fast convergence with complexity independent of the parameter dimension and the number of samples, strong parallel scalability in processor cores, and weak data scalability in the data dimension.

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

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