L'entraînement sans surveillance efficace et inférence dans les modèles génératifs profonds reste un problème difficile. Une approche assez simple, la machine de Helmholtz, consiste à entraîner du haut vers le bas un modèle génératif dirigé qui sera utilisé plus tard pour l'inférence approximative. Des résultats récents suggèrent que de meilleurs modèles génératifs peuvent être obtenus par de meilleures procédures d'inférence approximatives. Au lieu d'améliorer la procédure d'inférence, nous proposons ici un nouveau modèle, la machine de Helmholtz bidirectionnelle, qui garantit qu'on peut calculer efficacement les distributions de haut-vers-bas et de bas-vers-haut. Nous y parvenons en interprétant à les modèles haut-vers-bas et bas-vers-haut en tant que distributions d'inférence approximative, puis ensuite en définissant la distribution du modèle comme étant la moyenne géométrique de ces deux distributions. Nous dérivons une borne inférieure pour la vraisemblance de ce modèle, et nous démontrons que l'optimisation de cette borne se comporte en régulisateur. Ce régularisateur sera tel que la distance de Bhattacharyya sera minisée entre les distributions approximatives haut-vers-bas et bas-vers-haut. Cette approche produit des résultats de pointe en terme de modèles génératifs qui favorisent les réseaux significativement plus profonds. Elle permet aussi une inférence approximative amérliorée par plusieurs ordres de grandeur. De plus, nous introduisons un modèle génératif profond basé sur les modèles BiHM pour l'entraînement semi-supervisé. / Efficient unsupervised training and inference in deep generative models remains a challenging problem. One basic approach, called Helmholtz machine, involves training a top-down directed generative model together with a bottom-up auxiliary model used for approximate inference. Recent results indicate that better generative models can be obtained with better approximate inference procedures. Instead of improving the inference procedure, we here propose a new model, the bidirectional Helmholtz machine, which guarantees that the top-down and bottom-up distributions can efficiently invert each other. We achieve this by interpreting both the top-down and the bottom-up directed models as approximate inference distributions and by defining the model distribution to be the geometric mean of these two. We present a lower-bound for the likelihood of this model and we show that optimizing this bound regularizes the model so that the Bhattacharyya distance between the bottom-up and top-down approximate distributions is minimized. This approach results in state of the art generative models which prefer significantly deeper architectures while it allows for orders of magnitude more efficient approximate inference. Moreover, we introduce a deep generative model for semi-supervised learning problems based on BiHM models.

The problem of feature selection is critical in several areas of machine learning and data analysis such as, for example, cancer classification using gene expression data, text categorization, etc. In this work, we consider feature selection for supervised learning problems, where one wishes to select a small set of features that facilitate learning a good prediction model in the reduced feature space. Our interest is primarily in filter methods that select features independently of the learning algorithm to be used and are generally faster to implement compared to other types of feature selection algorithms. Many common filter methods for feature selection make use of information-theoretic criteria such as those based on mutual information to guide their search process. However, even in simple binary classification problems, mutual information based methods do not always select the best set of features in terms of the Bayes error. In this thesis, we develop a general approach for selecting a set of features that directly aims to minimize the Bayes error in the reduced feature space with respect to the loss or performance measure of interest. We show that the mutual information based criterion is a special case of our setting when the loss function of interest is the logarithmic loss for class probability estimation. We give a greedy forward algorithm for approximately optimizing this criterion and demonstrate its application to several supervised learning problems including binary classification (with 0-1 error, cost-sensitive error, and F-measure), binary class probability estimation (with logarithmic loss), bipartite ranking (with pairwise disagreement loss), and multiclass classification (with multiclass 0-1 error). Our experiments suggest that the proposed approach is competitive with several state-of-the art methods.