Improved finite-sample estimate of a nonparametric f-divergence

Information divergence functions allow us to measure distances between probability density functions. We focus on the case where we only have data from the two distributions and have no knowledge of the underlying models from which the data is sampled. In this scenario, we consider an f-divergence for which there exists an asymptotically consistent, nonparametric estimator based on minimum spanning trees, the D_p divergence. Nonparametric estimators are known to have slow convergence rates in higher dimensions (d > 4), resulting in a large bias for small datasets. Based on experimental validation, we conjecture that the original estimator follows a power law convergence model and introduce a new estimator based on a bootstrap sampling scheme that results in a reduced bias. Experiments on real and artificial data show that the new estimator results in improved estimates of the D_p divergence when compared against the original estimator.