On Margins and Derandomisation in PAC-Bayes
This work addresses theoretical challenges in machine learning by providing a general framework for derandomising PAC-Bayesian bounds, which is incremental as it builds on existing PAC-Bayes theory.
The paper tackles the problem of derandomising PAC-Bayesian bounds using margins, showing that randomised predictions concentrate around a value, leading to margin bounds for classifiers like linear predictors, neural networks with erf activation, and deep ReLU networks, with extensions to partially-derandomised predictors for cases with poor concentration.
We give a general recipe for derandomising PAC-Bayesian bounds using margins, with the critical ingredient being that our randomised predictions concentrate around some value. The tools we develop straightforwardly lead to margin bounds for various classifiers, including linear prediction -- a class that includes boosting and the support vector machine -- single-hidden-layer neural networks with an unusual \(\erf\) activation function, and deep ReLU networks. Further, we extend to partially-derandomised predictors where only some of the randomness is removed, letting us extend bounds to cases where the concentration properties of our predictors are otherwise poor.