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Bayesian Neural Networks

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Bayesian Neural Networks (BNNs) take a probabilistic approach to learning in neural networks by placing distributions over the weights and performing (approximate) Bayesian inference. In this talk, we will introduce the basics of BNNs, the challenges in training them, and some of their properties. We will then discuss the Laplace approximation as a highly performant approximate inference scheme for BNNs with connections to linear models and neural tangent kernels. Finally, we will provide a tour of prior choices in BNNs, looking at both weight and function space approaches.

Recommended reading:

MacKay, D. J. (1992). Bayesian interpolation. Neural computation, 4(3), 415-447.

Blundell, C., Cornebise, J., Kavukcuoglu, K., & Wierstra, D. (2015, June). Weight uncertainty in neural network. In International conference on machine learning (pp. 1613-1622). PMLR .

Immer, A., Korzepa, M., & Bauer, M. (2021, March). Improving predictions of Bayesian neural nets via local linearization. In International Conference on Artificial Intelligence and Statistics (pp. 703-711). PMLR .

Fortuin, V. (2022). Priors in bayesian deep learning: A review. International Statistical Review, 90(3), 563-591.

This talk is part of the Machine Learning Reading Group @ CUED series.

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