ABSTRACT
Undirected graphical models, also known as Markov random fields, have become a popular tool for representing network structure of high-dimensional data in a large variety of areas including genetics, brain network analysis, social networks and climate studies. Global methods estimate the precision matrix typically via a regularized log-likelihood, while nodewise methods split the problem into a series of linear regressions by estimating neighborhood of each node in the underlying graph. Inference for parameters in high-dimensional undirected graphical models was studied in several papers. A different approach to structure learning in undirected graphical models is the Hyvarinen score matching. The idea of nodewise Lasso is to estimate each column of the precision matrix by doing a projection of every column of the design matrix on all the remaining columns. While this is a pseudo-likelihood method, the decoupling into linear regressions gains more flexibility in estimating individual scaling levels compared to the graphical Lasso which aims to estimate all the parameters simultaneously.
