Progress in Self-Certified Neural Networks

Abstract: A learning method is self-certified if it uses all available data to simultaneously learn a predictor and certify its quality with a tight statistical certificate that is valid on unseen data. Recent work has shown that neural network models trained by optimising PAC-Bayes bounds lead not only to accurate predictors, but also to tight risk certificates, bearing promise towards achieving self-certified learning. In this context, learning and certification strategies based on PAC-Bayes bounds are especially attractive due to their ability to leverage all data to learn a posterior and simultaneously certify its risk with a tight numerical certificate. In this paper, we assess the progress towards self-certification in probabilistic neural networks learnt by PAC-Bayes inspired objectives. We empirically compare (on 4 classification datasets) classical test set bounds for deterministic predictors and a PAC-Bayes bound for randomised self-certified predictors. We first show that both of these generalisation bounds are not too far from out-of-sample test set errors. We then show that in data starvation regimes, holding out data for the test set bounds adversely affects generalisation performance, while self-certified strategies based on PAC-Bayes bounds do not suffer from this drawback, proving that they might be a suitable choice for the small data regime. We also find that probabilistic neural networks learnt by PAC-Bayes inspired objectives lead to certificates that can be surprisingly competitive with commonly used test set bounds.