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.
Learning Stochastic Majority Votes by Minimizing a PAC-Bayes Generalization Bound
Univ Lyon（里昂大学）；UJM-Saint-Etienne（圣埃蒂安让·莫内大学）；CNRS（法国国家科学研究中心）；Institut d Optique Graduate School（光学研究所研究生院）；Université Laval（拉瓦尔大学）；Inria（法国国家信息与自动化研究所）；Inria London Programme（法国国家信息与自动化研究所伦敦项目）；University College London（伦敦大学学院）
Reconcile Certified Robustness and Accuracy for DNN-based Smoothed Majority Vote Classifier
National Mobile Communications Research Laboratory, Southeast University, China（东南大学国家移动通信研究中心）；Department of Computer Science, University of Liverpool, UK（利物浦大学计算机科学系）
Université Laval（拉瓦尔大学）；Laboratoire Hubert Curien UMR CNRS 5516（于贝尔·居里安实验室 CNRS UMR 5516）；Univ. Jean Monnet（让·莫内大学）；Aix-Marseille Univ.（艾克斯-马赛大学）；CNRS（法国国家科学研究中心）
Domain adaptation of weighted majority votes via perturbed variation-based self-labeling
Institute of Science and Technology (IST) Austria（奥地利科学技术研究所）；University Jean Monnet of Saint-Etienne（圣艾蒂安让·莫内大学）；Laboratoire Hubert Curien UMR CNRS 5516（于贝尔·居里安实验室（法国国家科学研究中心联合研究单位5516））
Majority Vote for Distributed Differentially Private Sign Selection
School of Mathematics, Shanghai University of Finance and Economics（上海财经大学数学学院）；Ministry of Education Key Laboratory of Scientific and Engineering Computing, Shanghai Jiao Tong University（上海交通大学科学与工程计算教育部重点实验室）；Stern School of Business, New York University（纽约大学斯特恩商学院）
