Feature selection based on the best-path algorithm in high dimensional graphical models

This paper proposes a new algorithm for an automatic feature selection procedure in High Dimensional Graphical Models. The algorithm, called Best-Path Algorithm (BPA), rests on a filter method and performs feature selection based on mutual information.\r\nOver the last years, filter methods have been successfully employed to reduce the size of the input dataset and retain, at the same time, the relevant feature information for modelling and classification problems. \r\n \r\nHowever, the extant filter algorithms \r\nare mostly heuristic or require high computational effort. \r\nThe BPA overcomes these drawbacks by taking advantage of the links between variables brought to the fore by the Edwards's algorithm. \r\nOnce the High Dimensional Graphical Model, depicting the probabilistic structure of the variables, is determined, the BPA selects the best subset of features by analyzing its path-steps. \r\nThe path-step that includes the variables with the most predictive power for the target one is then determined via the computation of the entropy correlation coefficient. \r\nThis index, being based on the notion of (symmetric) Kullback-Leibler divergence, is closely connected to the mutual information that the path-step variables share with that of interest. \r\nThe BPA application \r\nto simulated and \r\nreal-word benchmark datasets highlights its potential and greater effectiveness compared to alternative extant methods.