Self-Bounding Majority Vote Learning Algorithms by the Direct Minimization of a Tight PAC-Bayesian C-Bound

Paul Viallard (1) , Pascal Germain (2) , Amaury Habrard (1) , Emilie Morvant (1)

1 LHC - Laboratoire Hubert Curien
2 ULaval - Université Laval [Québec]

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.

Domaines: Machine Learning [stat.ML]

Paul Viallard, Pascal Germain, Amaury Habrard, Emilie Morvant. Self-Bounding Majority Vote Learning Algorithms by the Direct Minimization of a Tight PAC-Bayesian C-Bound. ECML PKDD 2021, Sep 2021, Bilbao, Spain. ⟨hal-03208948v2⟩