Learning A Priori Constrained Weighted Majority Votes

Aurélien Bellet (1) , Amaury Habrard (2) , Emilie Morvant (3) , Marc Sebban (2)

1 USC - University of Southern California
2 LHC - Laboratoire Hubert Curien
3 IST Austria - Institute of Science and Technology [Klosterneuburg, Austria]

Weighted majority votes allow one to combine the output of several classifiers or voters. MinCq is a recent algorithm for optimizing the weight of each voter based on the minimization of a theoretical bound over the risk of the vote with elegant PAC-Bayesian generalization guarantees. However, while it has demonstrated good performance when combining weak classifiers, MinCq cannot make use of the useful a priori knowledge that one may have when using a mixture of weak and strong voters. In this paper, we propose P-MinCq, an extension of MinCq that can incorporate such knowledge in the form of a constraint over the distribution of the weights, along with general proofs of convergence that stand in the sample compression setting for data-dependent voters. The approach is applied to a vote of k-NN classifiers with a specific modeling of the voters' performance. P-MinCq significantly outperforms the classic k-NN classifier, a symmetric NN and MinCq using the same voters. We show that it is also competitive with LMNN, a popular metric learning algorithm, and that combining both approaches further reduces the error.

Mots clés: Ensemble learning; Weighted majority vote; PAC-Bayesian bounds; Sample compression; Nearest neighbors

Domaines: Machine Learning [stat.ML]

Aurélien Bellet, Amaury Habrard, Emilie Morvant, Marc Sebban. Learning A Priori Constrained Weighted Majority Votes. Machine Learning, 2014, 97 (1-2), pp.129-154. ⟨10.1007/s10994-014-5462-z⟩. ⟨hal-01009578⟩