ℓ1-Penalized Methods in High-Dimensional Gaussian Markov Random Fields

In the last 20 years, we have witnessed the dramatic development of new data acquisition technologies allowing to collect massive amount of data with relatively low cost. is new feature leads Donoho to define the twenty-first century as the century of data. A major characteristic of this modern data set is that the number of measured variables is larger than the sample size; the word high-dimensional data analysis is referred to the statistical methods developed to make inference with this new kind of data. This chapter is devoted to the study of some of the most recent ℓ1-penalized methods proposed in the literature to make sparse inference in a Gaussian Markov random field (GMRF) defined in a high-dimensional setting. Special emphasis is given both to the computational aspects and to the packages developed for the statistical software R.