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arXiv · 1908.07380

PAC-Bayes with Backprop

Omar Rivasplata·Vikram M Tankasali·Csaba Szepesvari
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Abstract

We explore the family of methods "PAC-Bayes with Backprop" (PBB) to train probabilistic neural networks by minimizing PAC-Bayes bounds. We present two training objectives, one derived from a previously known PAC-Bayes bound, and a second one derived from a novel PAC-Bayes bound. Both training objectives are evaluated on MNIST and on various UCI data sets. Our experiments show two striking observations: we obtain competitive test set error estimates (~1.4% on MNIST) and at the same time we compute non-vacuous bounds with much tighter values (~2.3% on MNIST) than previous results. These observations suggest that neural nets trained by PBB may lead to self-bounding learning, where the available data can be used to simultaneously learn a predictor and certify its risk, with no need to follow a data-splitting protocol.

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Omar Rivasplata, Vikram M Tankasali, Csaba Szepesvari. 2019-08-19. PAC-Bayes with Backprop. https://arxiv.org/abs/1908.07380

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