  This paper proposes a new algorithm for an automatic variable selection
procedure in High Dimensional Graphical Models. The algorithm selects the
relevant variables for the node of interest on the basis of mutual information.
Several contributions in literature have investigated the use of mutual
information in selecting the appropriate number of relevant features in a large
data-set, but most of them have focused on binary outcomes or required high
computational effort. The algorithm here proposed overcomes these drawbacks as
it is an extension of Chow and Liu's algorithm. Once, the probabilistic
structure of a High Dimensional Graphical Model is determined via the said
algorithm, the best path-step, including variables with the most
explanatory/predictive power for a variable of interest, is determined via the
computation of the entropy coefficient of determination. The latter, being
based on the notion of (symmetric) Kullback-Leibler divergence, turns out to be
closely connected to the mutual information of the involved variables. The
application of the algorithm to a wide range of real-word and publicly
data-sets has highlighted its potential and greater effectiveness compared to
alternative extant methods.
