PAC-Bayesian Transportation Bound
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We present a new generalization error bound, the PAC-Bayesian transportation bound, unifying the PAC-Bayesian analysis and the generic chaining method in view of the optimal transportation. The proposed bound is the first PAC-Bayesian framework that characterizes the cost of de-randomization of stochastic predictors facing any Lipschitz loss functions. As an example, we give an upper bound on the de-randomization cost of spectrally normalized neural networks (NNs) to evaluate how much randomness contributes to the generalization of NNs.
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