Estimation of Renyi information divergence via pruned minimal spanning trees

In this paper we develop robust estimators of the Renyi information divergence (I-divergence) given a reference distribution and a random sample from an unknown distribution. Estimation is performed by constructing a minimal spanning tree (MST) passing through the random sample points and applying a change of measure which flattens the reference distribution. In a mixture model where the reference distribution is contaminated by an unknown noise distribution one can use these results to reject noise samples by implementing a greedy algorithm for pruning the k-longest branches of the MST, resulting in a tree called the k-MST. We illustrate this procedure in the context of density discrimination and robust clustering for a planar mixture model