Bayesian Prior Networks with PAC Training
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We propose to train Bayesian Neural Networks (BNNs) by empirical Bayes as an alternative to posterior weight inference. By approximately marginalizing out an i.i.d. realization of a finite number of sibling weights per data-point using the Central Limit Theorem (CLT), we attain a scalable and effective Bayesian deep predictor. This approach directly models the posterior predictive distribution, by-passing the intractable posterior weight inference step. However, it introduces a prohibitively large number of hyperparameters for stable training. As the prior weights are marginalized and hyperparameters are optimized, the model also no longer provides a means to incorporate prior knowledge. We overcome both of these drawbacks by deriving a trivial PAC bound that comprises the marginal likelihood of the predictor and a complexity penalty. The outcome integrates organically into the prior networks framework, bringing about an effective and holistic Bayesian treatment of prediction uncertainty. We observe on various regression, classification, and out-of-domain detection benchmarks that our scalable method provides an improved model fit accompanied with significantly better uncertainty estimates than the state-of-the-art.
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