Self-Bounding Majority Vote Learning Algorithms by the Direct Minimization of a Tight PAC-Bayesian C-Bound
This work addresses the need for more reliable and theoretically grounded learning algorithms in machine learning, though it appears incremental as it builds on existing PAC-Bayesian frameworks.
The paper tackles the problem of learning majority vote classifiers by directly optimizing PAC-Bayesian generalization bounds on the C-Bound, resulting in scalable gradient descent algorithms that produce accurate predictors with non-vacuous guarantees.
In the PAC-Bayesian literature, the C-Bound refers to an insightful relation between the risk of a majority vote classifier (under the zero-one loss) and the first two moments of its margin (i.e., the expected margin and the voters' diversity). Until now, learning algorithms developed in this framework minimize the empirical version of the C-Bound, instead of explicit PAC-Bayesian generalization bounds. In this paper, by directly optimizing PAC-Bayesian guarantees on the C-Bound, we derive self-bounding majority vote learning algorithms. Moreover, our algorithms based on gradient descent are scalable and lead to accurate predictors paired with non-vacuous guarantees.