Half a century ago, Chow and Liu proved that the distribution of the first-order dependence tree that optimally approximates an arbitrary joint distribution in terms of Kullback–Leibler cross entropy is the distribution of the maximum-weight dependence tree (MWDT). In a   $p$   -dimensional space, this is a tree with   $p-1$    branches between pairs of variables with each branch having a weight equal to the mutual information between variables at both ends. Today, MWDTs have applications that are more important in classification than only being used to model first-order dependence structure among variables. Nevertheless, whether the MWDT is the optimal first-order tree in classification has been left unexplored so far. In this letter, we study the optimality of the MWDT structure from the stand-point of classification.
['Amin Zollanvari']
Nonoptimality of the Maximum-Weight Dependence Tree in Classification