The overall aim of this research project is the development of statistical learning methods that take into account the characteristics of fMRI data, and that can be used for inverse inference. From an experimental point of view, we particularly focus on the understanding of the human visual cortex, but the presented frameworks can be used to study any brain system.
Functional brain imaging (or Neuroimaging) provides a unique opportunity to study brain functional architecture, while being minimally invasive, and is thus well-suited for the challenging study of the spatial layout of neural coding. Different modalities exist, each one having speciﬁc spatial and temporal resolutions; among them Functional Magnetic Resonance Imaging (fMRI) has emerged as a fundamental modality for brain imaging. Over the last two decades, fMRI [Ogawa 90b, Ogawa 90a] has been widely used for brain imaging, and has become a reference method for neuroscientiﬁc studies, due to its good spatial resolution. fMRI images are pre-processed, and modeled through a General Linear Model, that takes into account the different experimental conditions and the dynamics of the hemodynamic response in the design matrix. The resulting model parameters, a.k.a. activation maps, represent the inﬂuence of the different experimental conditions on local fMRI signals.
The classical and widely used approach for analyzing these activation maps is called classical inference, and relies on a mass-univariate statistical tests (one for each voxel), yielding the so-called Statistical Parametric Maps (SPMs) [Friston 95]. Such maps are of particular interest in neurosciences, as they open the door to localizing the voxels that are signiﬁcantly active for any combination of experimental conditions, and thus are probably implied in the underlying neural code of the cognitive processes. However, this classical inference suffers from multiple comparisons issues, and does not take into account the multivariate structure of the fMRI data.
A recent approach, called inverse inference (or ”brain-reading”) [Dehaene 98, Cox 03], has been proposed in order to cope with the limitations of the classical inference. Inverse inference relies on a pattern recognition framework, and aims at decoding the neural code by using statistical learning methods. Based on a set of activation maps, inverse inference builds a prediction function that can be used for predicting a behavioral target for a new set of images. The resulting prediction accuracy is a measure of the quantity of information about the cognitive task shared by the voxels. This approach is multivariate, and can provide more sensitive analysis than standard statistical parametric mapping procedure [Kamitani 05, Haynes 06]. Many methods have been tested for classiﬁcation or regression of activation images (Linear Discriminant Analysis, Support Vector Machines, Lasso, Elastic net regression, and many others), but, in this problem, the major bottleneck remains the localization of predictive regions within the brain volume. Additionally, we have to deal with the curse of dimensionality, as the number of features (voxels, regions) is much larger (∼ 100.000 ) than the numbers of samples (images) (∼ 100 ), and thus the prediction method may overﬁt the training set and thus not generalize well to new samples.