Risk Bounds for the Majority Vote: From a PAC-Bayesian Analysis to a Learning Algorithm
This work provides a theoretical foundation for majority vote learning, addressing a core problem in ensemble methods for binary classification, though it is incremental in extending PAC-Bayesian analysis.
The paper tackles the analysis of majority votes in binary classification by introducing the C-bound risk bound, which accounts for voter quality and disagreement, and develops the MinCq algorithm to minimize this bound. The algorithm achieves state-of-the-art performance, outperforming AdaBoost and SVM in empirical comparisons.
We propose an extensive analysis of the behavior of majority votes in binary classification. In particular, we introduce a risk bound for majority votes, called the C-bound, that takes into account the average quality of the voters and their average disagreement. We also propose an extensive PAC-Bayesian analysis that shows how the C-bound can be estimated from various observations contained in the training data. The analysis intends to be self-contained and can be used as introductory material to PAC-Bayesian statistical learning theory. It starts from a general PAC-Bayesian perspective and ends with uncommon PAC-Bayesian bounds. Some of these bounds contain no Kullback-Leibler divergence and others allow kernel functions to be used as voters (via the sample compression setting). Finally, out of the analysis, we propose the MinCq learning algorithm that basically minimizes the C-bound. MinCq reduces to a simple quadratic program. Aside from being theoretically grounded, MinCq achieves state-of-the-art performance, as shown in our extensive empirical comparison with both AdaBoost and the Support Vector Machine.