# PAC-Bayesian Transportation Bound

arXiv: https://arxiv.org/abs/1905.13435 · HTML: https://mlsanity.com/paper/1905.13435/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 May 2019.

## Built on by (most cited first, 3 of 3)

- [Integral Probability Metrics PAC-Bayes Bounds](https://mlsanity.com/paper/2207.00614/) (2022)
- [PAC-Bayes Bounds for Meta-learning with Data-Dependent Prior](https://mlsanity.com/paper/2102.03748/) (2021)
- [Generalisation under gradient descent via deterministic PAC-Bayes](https://mlsanity.com/paper/2209.02525/) (2022)

## Abstract (arXiv)

Empirically, the PAC-Bayesian analysis is known to produce tight risk bounds for practical machine learning algorithms. However, in its naive form, it can only deal with stochastic predictors while such predictors are rarely used and deterministic predictors often performs well in practice. To fill this gap, we develop a new generalization error bound, the PAC-Bayesian transportation bound, unifying the PAC-Bayesian analysis and the chaining method in view of the optimal transportation. It is the first PAC-Bayesian bound that relates the risks of any two predictors according to their distance, and capable of evaluating the cost of de-randomization of stochastic predictors faced with continuous 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.