Generalized Variational Inference in Function Spaces: Gaussian Measures meet Bayesian Deep Learning. (arXiv:2205.06342v1 [stat.ML])

We develop a framework for generalized variational inference in
infinite-dimensional function spaces and use it to construct a method termed
Gaussian Wasserstein inference (GWI). GWI leverages the Wasserstein distance
between Gaussian measures on the Hilbert space of square-integrable functions
in order to determine a variational posterior using a tractable optimisation
criterion and avoids pathologies arising in standard variational function space
inference. An exciting application of GWI is the ability to use deep neural
networks in the variational parametrisation of GWI, …

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