Feature extraction and supervised learning on fMRI : from practice to theory.

Summary Until the advent of non-invasive neuroimaging methods, knowledge of the brain was acquired through the study of its lesions, post-mortem analyses and invasive experiments. Nowadays, modern imaging techniques such as fMRI are able to reveal many aspects of the human brain at a progressively higher spatio-temporal resolution. However, in order to answer increasingly complex neuroscientific questions, technical improvements in acquisition must be coupled with new methods of data analysis. In this thesis, I propose different applications of statistical learning to fMRI data processing. Often, the data acquired by the fMRI scanner follows a variable selection step in which activation maps are extracted from the fMRI signal. The first contribution of this thesis is the introduction of a model named Rank-1 GLM (R1-GLM) for the joint estimation of activation maps and the hemodynamic response function (HRF). We quantify the improvement of this approach over existing procedures on different fMRI datasets. The second part of this thesis is devoted to the decoding problem in fMRI, i.e., the task of predicting some information about the stimuli from the brain activation maps. From a statistical point of view, this problem is difficult due to the high dimensionality of the data, often thousands of variables, while the number of images available for training is small, typically a few hundred. We consider the case where the target variable is composed from discrete and ordered values. The second contribution of this thesis is to propose the following two measures to evaluate the performance of a decoding model: absolute error and pairwise detuning. We present several models that optimize a convex approximation of these loss functions and examine their performance on fMRI data sets. Motivated by the success of some ordinal regression models for the fMRI-based decoding task, we turn to the study of some theoretical properties of these methods. The property we study is known as Fisher consistency. The third, and most theoretical, contribution of this thesis is to examine the consistency properties of a rich family of loss functions that are used in ordinal regression models.