Inproceedings,
Estimation of Rényi Entropy and Mutual Information Based on Generalized Nearest-Neighbor Graphs (extended version)
NIPS, (December 2010)
Abstract
We present simple and computationally efficient nonparametric estimators of
Rényi entropy and mutual information based on an i.i.d. sample drawn from an
unknown, absolutely continuous distribution over R^d. The estimators are
calculated as the sum of p-th powers of the Euclidean lengths of the edges of
the `generalized nearest-neighbor' graph of the sample and the empirical copula
of the sample respectively. For the first time,
we prove the almost sure consistency of these estimators and
upper bounds on their rates of convergence, the latter of which under
the assumption that the density underlying the sample is Lipschitz continuous.
Experiments demonstrate their usefulness in independent subspace analysis.
