A primary goal in systems neuroscience is to understand how neural spike responses encode information about the external world. A popular approach to this problem is to build an explicit probabilistic model that characterizes the encoding relationship in terms of a cascade of stages: (1) linear dimensionality reduction of a high-dimensional stimulus space using a bank of filters or receptive fields (RFs); (2) a nonlinear function from filter outputs to spike rate; and (3) a stochastic spiking process with recurrent feedback. These models have described single- and multi-neuron spike responses in a wide variety of brain areas. This dissertation addresses Bayesian methods to efficiently estimate the linear and non-linear stages of the cascade encoding model. In the first part, the dissertation describes a novel Bayesian receptive field estimator based on a hierarchical prior that flexibly incorporates knowledge about the shapes of neural receptive fields. This estimator achieves error rates several times lower than existing methods, and can be applied to a variety of other neural inference problems such as extracting structure in fMRI data. The dissertation also presents active learning frameworks developed for receptive field estimation incorporating a hierarchical prior in real-time neurophysiology experiments. In addition, the dissertation describes a novel low-rank model for the high dimensional receptive field, combined with a hierarchical prior for more efficient receptive field estimation. In the second part, the dissertation describes new models for neural nonlinearities using Gaussian processes (GPs) and Bayesian active learning algorithms in closed-loop neurophysiology experiments to rapidly estimate neural nonlinearities. The dissertation also presents several stimulus selection criteria and compare their performance in neural nonlinearity estimation. Furthermore, the dissertation presents a variation of the new models by including an additional latent Gaussian noise source, to infer the degree of over-dispersion in neural spike responses. The proposed model successfully captures various mean-variance relationships in neural spike responses and achieves higher prediction accuracy than previous models. / text

Dans les applications modernes des statistiques et de l'apprentissage, il est courant que les données récoltées présentent un certain nombre d'imperfections. En particulier, les données sont souvent hétérogènes, c'est-à-dires qu'elles contiennent à la fois des informations quantitatives et qualitatives, incomplètes, lorsque certaines informations sont inaccessibles ou corrompues, et multi-sources, c'est-à-dire qu'elles résultent de l'agrégation de plusieurs jeux de données indépendant. Dans cette thèse, nous développons plusieurs méthodes pour l'analyse de données hétérogènes, incomplètes et multi-source. Nous nous attachons à étudier tous les aspects de ces méthodes, en fournissant des études théoriques précises, ainsi que des implémentations disponibles au public, et des évaluations empiriques. En particulier, nous considérons en détail deux applications issues de l'écologie pour la première et de la médecine pour la seconde. / In modern applications of statistics and machine learning, one often encounters many data imperfections. In particular, data are often heterogeneous, i.e. combine quantitative and qualitative information, incomplete, with missing values caused by machine failure or nonresponse phenomenons, and multi-source, when the data result from the compounding of diverse sources. In this dissertation, we develop several methods for the analysis of multi-source, heterogeneous and incomplete data. We provide a complete framework, and study all the aspects of the different methods, with thorough theoretical studies, open source implementations, and empirical evaluations. We study in details two particular applications from ecology and medical sciences.