Implicit Functional Bayesian Deep Learning
Keywords: Bayesian Deep Learning, function space, variational inference
Abstract: Bayesian deep learning (BDL) is believed to be an effective approach to enabling uncertainty estimation and improving the generalisation and robustness of classical deep learning with the help of the Bayesian principle. Considering its non-meaningful weight-space prior and problematic Kullback-Leibler (KL) divergence, functional inference with Wasserstein distance has recently emerged as a promising direction in this field. However, existing efforts require different types of degenerations to achieve tractable Wasserstein distance computation, which limits the predictive and uncertainty estimation capabilities. In this paper, we propose two novel implicit functional BDL (ifBDL) approaches, i.e., implicit functional Bayesian neural networks and implicit functional Bayesian deep ensemble. The common idea is to implicitly transform the BDL posterior to a Gaussian process via the neural tangent kernel to facilitate tractable 2-Wasserstein distance computation and preserve the neural network parameterization. The experimental evaluations on standard tasks show that ifBDL has superior predictive and uncertainty estimation capabilities compared to existing weight-space and function-space approaches.
Supplementary Material: zip
Primary Area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)
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Submission Number: 4347
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