Generalized Variational Inference in Function Spaces: Gaussian Measures meet Bayesian Deep Learning
This provides a method for combining deep learning with Gaussian process-like uncertainty quantification, addressing a key challenge in Bayesian deep learning for improved predictive reliability.
The paper tackles the problem of variational inference in infinite-dimensional function spaces by introducing Gaussian Wasserstein inference (GWI), which uses the Wasserstein distance between Gaussian measures to avoid pathologies and enable deep neural networks for principled uncertainty quantification, achieving state-of-the-art performance on benchmark datasets.
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, combining their superior predictive performance with the principled uncertainty quantification analogous to that of Gaussian processes. The proposed method obtains state-of-the-art performance on several benchmark datasets.