Uncovering sparse brain effective connectivity: A voxel-based approach using penalized regression

The processing of massive data generated by bioinformatic and neuroscience studies is a current challenge to statisticians since they require the development of computationally efficient and stable algorithms that can deal with many more variables than observations. In neuroscience, a clear example of this situation is the estimation of brain physiological interactions through the analysis of fMRI time series. The widespread use of the General Linear Model in the resolution of these problems has now been enhanced by the addition of prior assumptions, such as the sparseness and/or the spatiotemporal smoothness of a desirable solution (Valdes-Sosa (2004)). In this context, the use of Local Quadratic Approximation (LQA) (Fan and Li (2001)) and the Minorization- Maximization (MM) Hunter and Li (2005)) algorithms are practical ways for estimating the sparse models. Recently, we have extended these techniques to allow the combination of these attractive properties (Valdes-Sosa et al. (2006)). Here, we further formalize the methods and introduce a feature selection algorithm for feasible implementation. The methodology is then applied to the estimation of voxel-based brain effective connectivity using simulated and neuroimaging data.