  Recent works have investigated deep learning models trained by optimising
PAC-Bayes bounds, with priors that are learnt on subsets of the data. This
combination has been shown to lead not only to accurate classifiers, but also
to remarkably tight risk certificates, bearing promise towards self-certified
learning (i.e. use all the data to learn a predictor and certify its quality).
In this work, we empirically investigate the role of the prior. We experiment
on 6 datasets with different strategies and amounts of data to learn
data-dependent PAC-Bayes priors, and we compare them in terms of their effect
on test performance of the learnt predictors and tightness of their risk
certificate. We ask what is the optimal amount of data which should be
allocated for building the prior and show that the optimum may be dataset
dependent. We demonstrate that using a small percentage of the prior-building
data for validation of the prior leads to promising results. We include a
comparison of underparameterised and overparameterised models, along with an
empirical study of different training objectives and regularisation strategies
to learn the prior distribution.
