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Differentiable PAC-Bayes Objectives with Partially Aggregated Neural Networks

Felix Biggs 1, 2 Benjamin Guedj 3, 1, 4, 5, 2 
5 MODAL - MOdel for Data Analysis and Learning
LPP - Laboratoire Paul Painlevé - UMR 8524, Université de Lille, Sciences et Technologies, Inria Lille - Nord Europe, METRICS - Evaluation des technologies de santé et des pratiques médicales - ULR 2694, Polytech Lille - École polytechnique universitaire de Lille
Abstract : We make three related contributions motivated by the challenge of training stochastic neural networks, particularly in a PAC-Bayesian setting: (1) we show how averaging over an ensemble of stochastic neural networks enables a new class of \emph{partially-aggregated} estimators; (2) we show that these lead to provably lower-variance gradient estimates for non-differentiable signed-output networks; (3) we reformulate a PAC-Bayesian bound for these networks to derive a directly optimisable, differentiable objective and a generalisation guarantee, without using a surrogate loss or loosening the bound. This bound is twice as tight as that of Letarte et al. (2019) on a similar network type. We show empirically that these innovations make training easier and lead to competitive guarantees.
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Felix Biggs, Benjamin Guedj. Differentiable PAC-Bayes Objectives with Partially Aggregated Neural Networks. Entropy, MDPI, 2021, ⟨10.3390/e23101280⟩. ⟨hal-02879216⟩

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