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Traditionally, kernel methods rely on the representer theorem which states that the solution to a learning problem is obtained as a linear combination of the data mapped into the reproducing kernel Hilbert space (RKHS). While elegant from theoretical point of view, the theorem is prohibitive for algorithms' scalability to large datasets, and the interpretability of the learned function. In this paper, instead of using the traditional representer theorem, we propose to search for a solution in RKHS that has a pre-image decomposition in the original data space, where the elements don't necessarily correspond to the elements in the training set. Our gradient-based optimisation method then hinges on optimising over possibly sparse elements in the input space, and enables us to obtain a kernel-based model with both primal and dual sparsity. We give theoretical justification on the proposed method's generalization ability via a Rademacher bound. Our experiments demonstrate a better scalability and interpretability with accuracy on par with the traditional kernel-based models.

International audience; We consider the problem of metric learning for multi-view data and present a novel method for learning within-view as well as between-view metrics in vector-valued kernel spaces, as a way to capture multi-modal structure of the data. We formulate two convex optimization problems to jointly learn the metric and the classifier or regressor in kernel feature spaces. An iterative three-step multi-view metric learning algorithm is derived from the optimization problems. In order to scale the computation to large training sets, a block-wise Nyström approximation of the multi-view kernel matrix is introduced. We justify our approach theoretically and experimentally, and show its performance on real-world datasets against relevant state-of-the-art methods.

In imbalanced multi-class classification problems, the misclassification rate as an error measure may not be a relevant choice. Several methods have been developed where the performance measure retained richer information than the mere misclassification rate: misclassification costs, ROC-based information, etc. Following this idea of dealing with alternate measures of performance, we propose to address imbalanced classification problems by using a new measure to be optimized: the norm of the confusion matrix. Indeed, recent results show that using the norm of the confusion matrix as an error measure can be quite interesting due to the fine-grain informations contained in the matrix, especially in the case of imbalanced classes. Our first contribution then consists in showing that optimizing criterion based on the confusion matrix gives rise to a common background for cost-sensitive methods aimed at dealing with imbalanced classes learning problems. As our second contribution, we propose an extension of a recent multi-class boosting method --- namely AdaBoost.MM --- to the imbalanced class problem, by greedily minimizing the empirical norm of the confusion matrix. A theoretical analysis of the properties of the proposed method is presented, while experimental results illustrate the behavior of the algorithm and show the relevancy of the approach compared to other methods.

The ability of vaccine antigen to generate protection is a challenge that cannot be restricted to the antibody response; however, the contribution of T cell-mediated mechanisms has not been extensively analyzed. Age and administration to specific categories of patients, i.e. children with recurrent infections (RI), are some of the factors that might affect the vaccine immune response. We investigated the humoral and cellular response to tetanus toxoid (TT) vaccine in 104 healthy children (HC), 11 newborns and 22 healthy adults to characterize the status of immunity according to age and compared it to 118 RI children. Humoral and cellular responses varied in both groups according to age and doses of TT administered. The prevalence of antibody and cellular response was similar in both cohorts (HC 88 percent and 82 percent versus RI 86 percent and 85 percent), however, TT antibody values were significantly higher in 12-18 months old RI children compared to HC (median: 5 IU/ml vs 1.10 IU/ml) (p = 0.02). The lack of an efficient immune response was observed in 12-15 percent of children from both cohorts. Our data showed that specific antibodies were responsible for early protection, whereas cell-mediated mechanisms may contribute to the generation of long-term immunity after an appropriate vaccine recall. The occurrence of higher TT antibody values in 12-18 months old RI children deserves additional research to determine whether they are caused by different infectious agents and/or by other environmental factors. Clarification of this issue is important for categorizing patients into an optimal vaccine policy.