Bayesian Neural Networks With Maximum Mean Discrepancy Regularization

• URL: http://arxiv.org/abs/2003.00952v2
• Date: Wed, 30 Sep 2020 09:56:44 GMT
• Title: Bayesian Neural Networks With Maximum Mean Discrepancy Regularization
• Authors: Jary Pomponi, Simone Scardapane, and Aurelio Uncini
• Abstract summary: We show that our BNNs achieve higher accuracy on multiple benchmarks, including several image classification tasks. We also provide a new formulation for estimating the uncertainty on a given prediction, showing it performs in a more robust fashion against adversarial attacks.
• Score: 13.97417198693205
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Bayesian Neural Networks (BNNs) are trained to optimize an entire distribution over their weights instead of a single set, having significant advantages in terms of, e.g., interpretability, multi-task learning, and calibration. Because of the intractability of the resulting optimization problem, most BNNs are either sampled through Monte Carlo methods, or trained by minimizing a suitable Evidence Lower BOund (ELBO) on a variational approximation. In this paper, we propose a variant of the latter, wherein we replace the Kullback-Leibler divergence in the ELBO term with a Maximum Mean Discrepancy (MMD) estimator, inspired by recent work in variational inference. After motivating our proposal based on the properties of the MMD term, we proceed to show a number of empirical advantages of the proposed formulation over the state-of-the-art. In particular, our BNNs achieve higher accuracy on multiple benchmarks, including several image classification tasks. In addition, they are more robust to the selection of a prior over the weights, and they are better calibrated. As a second contribution, we provide a new formulation for estimating the uncertainty on a given prediction, showing it performs in a more robust fashion against adversarial attacks and the injection of noise over their inputs, compared to more classical criteria such as the differential entropy.

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