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This paper proposes a new algorithm for an automatic variable selectionprocedure in High Dimensional Graphical Models. The algorithm selects therelevant variables for the node of interest on the basis of mutual information.Several contributions in literature have investigated the use of mutualinformation in selecting the appropriate number of relevant features in a largedata-set, but most of them have focused on binary outcomes or required highcomputational effort. The algorithm here proposed overcomes these drawbacks asit is an extension of Chow and Liu's algorithm. Once, the probabilisticstructure of a High Dimensional Graphical Model is determined via the saidalgorithm, the best path-step, including variables with the mostexplanatory/predictive power for a variable of interest, is determined via thecomputation of the entropy coefficient of determination. The latter, beingbased on the notion of (symmetric) Kullback-Leibler divergence, turns out to beclosely connected to the mutual information of the involved variables. Theapplication of the algorithm to a wide range of real-word and publiclydata-sets has highlighted its potential and greater effectiveness compared toalternative extant methods.

The Best Path Algorithm automatic variables selection via High Dimensional Graphical Models