A Unified View of Local Learning : Theory and Algorithms for Enhancing Linear Models. (Une Vue Unifiée de l'Apprentissage Local : Théorie et Algorithmes pour l'Amélioration de Modèles Linéaires)

In Machine Learning field, data characteristics usually vary over the space: the overall distribution might be multi-modal and contain non-linearities.In order to achieve good performance, the learning algorithm should then be able to capture and adapt to these changes. Even though linear models fail to describe complex distributions, they are renowned for their scalability, at training and at testing, to datasets big in terms of number of examples and of number of features. Several methods have been proposed to take advantage of the scalability and the simplicity of linear hypotheses to build models with great discriminatory capabilities. These methods empower linear models, in the sense that they enhance their expressive power through different techniques. This dissertation focuses on enhancing local learning approaches, a family of techniques that infers models by capturing the local characteristics of the space in which the observations are embedded. The founding assumption of these techniques is that the learned model should behave consistently on examples that are close, implying that its results should also change smoothly over the space. The locality can be defined on spatial criteria (e.g. closeness according to a selected metric) or other provided relations, such as the association to the same category of examples or a shared attribute. Local learning approaches are known to be effective in capturing complex distributions of the data, avoiding to resort to selecting a model specific for the task. However, state of the art techniques suffer from three major drawbacks: they easily memorize the training set, resulting in poor performance on unseen data; their predictions lack of smoothness in particular locations of the space;they scale poorly with the size of the datasets. The contributions of this dissertation investigate the aforementioned pitfalls in two directions: we propose to introduce side information in the problem formulation to enforce smoothness in prediction and attenuate the memorization phenomenon; we provide a new representation for the dataset which takes into account its local specificities and improves scalability. Thorough studies are conducted to highlight the effectiveness of the said contributions which confirmed the soundness of their intuitions. We empirically study the performance of the proposed methods both on toy and real tasks, in terms of accuracy and execution time, and compare it to state of the art results. We also analyze our approaches from a theoretical standpoint, by studying their computational and memory complexities and by deriving tight generalization bounds.