Fast Multidimensional Entropy Estimation by $k$-d Partitioning

We describe a nonparametric estimator for the differential entropy of a multidimensional distribution, given a limited set of data points, by a recursive rectilinear partitioning. The estimator uses an adaptive partitioning method and runs in Theta(
N

_log

N
) time, with low memory requirements. In experiments using known distributions, the estimator is several orders of magnitude faster than other estimators, with only modest increase in bias and variance.