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.

In machine learning, the domain adaptation problem arrives when the test (target) and the train (source) data are generated from different distributions. A key applied issue is thus the design of algorithms able to generalize on a new distribution, for which we have no label information. We focus on learning classification models defined as a weighted majority vote over a set of real-val ued functions. In this context, Germain et al. (2013) have shown that a measure of disagreement between these functions is crucial to control. The core of this measure is a theoretical bound--the C-bound (Lacasse et al., 2007)--which involves the disagreement and leads to a well performing majority vote learning algorithm in usual non-adaptative supervised setting: MinCq. In this work, we propose a framework to extend MinCq to a domain adaptation scenario. This procedure takes advantage of the recent perturbed variation divergence between distributions proposed by Harel and Mannor (2012). Justified by a theoretical bound on the target risk of the vote, we provide to MinCq a target sample labeled thanks to a perturbed variation-based self-labeling focused on the regions where the source and target marginals appear similar. We also study the influence of our self-labeling, from which we deduce an original process for tuning the hyperparameters. Finally, our framework called PV-MinCq shows very promising results on a rotation and translation synthetic problem.

In the past few years, a lot of attention has been devoted to multimedia indexing by fusing multimodal informations. Two kinds of fusion schemes are generally considered: The early fusion and the late fusion. We focus on late classifier fusion, where one combines the scores of each modality at the decision level. To tackle this problem, we investigate a recent and elegant well-founded quadratic program named MinCq coming from the machine learning PAC-Bayesian theory. MinCq looks for the weighted combination, over a set of real-valued functions seen as voters, leading to the lowest misclassification rate, while maximizing the voters' diversity. We propose an extension of MinCq tailored to multimedia indexing. Our method is based on an order-preserving pairwise loss adapted to ranking that allows us to improve Mean Averaged Precision measure while taking into account the diversity of the voters that we want to fuse. We provide evidence that this method is naturally adapted to late fusion procedures and confirm the good behavior of our approach on the challenging PASCAL VOC'07 benchmark.

We tackle the PAC-Bayesian Domain Adaptation (DA) problem. This arrives when one desires to learn, from a source distribution, a good weighted majority vote (over a set of classifiers) on a different target distribution. In this context, the disagreement between classifiers is known crucial to control. In non-DA supervised setting, a theoretical bound - the C-bound - involves this disagreement and leads to a majority vote learning algorithm: MinCq. In this work, we extend MinCq to DA by taking advantage of an elegant divergence between distribution called the Perturbed Varation (PV). Firstly, justified by a new formulation of the C-bound, we provide to MinCq a target sample labeled thanks to a PV-based self-labeling focused on regions where the source and target marginal distributions are closer. Secondly, we propose an original process for tuning the hyperparameters. Our framework shows very promising results on a toy problem.

A lot of attention has been devoted to multimedia indexing over the past few years. In the literature, we often consider two kinds of fusion schemes: The early fusion and the late fusion. In this paper we focus on late classifier fusion, where one combines the scores of each modality at the decision level. To tackle this problem, we investigate a recent and elegant well-founded quadratic program named MinCq coming from the Machine Learning PAC-Bayes theory. MinCq looks for the weighted combination, over a set of real-valued functions seen as voters, leading to the lowest misclassification rate, while making use of the voters' diversity. We provide evidence that this method is naturally adapted to late fusion procedure. We propose an extension of MinCq by adding an order- preserving pairwise loss for ranking, helping to improve Mean Averaged Precision measure. We confirm the good behavior of the MinCq-based fusion approaches with experiments on a real image benchmark.