Divergence Estimation for Multidimensional Densities Via k-Nearest-Neighbor Distances

A new universal estimator of divergence is presented for multidimensional continuous densities based on k -nearest-neighbor ( k -NN) distances. Assuming independent and identically distributed (i.i.d.) samples, the new estimator is proved to be asymptotically unbiased and mean-square consistent. In experiments with high-dimensional data, the k -NN approach generally exhibits faster convergence than previous algorithms. It is also shown that the speed of convergence of the k -NN method can be further improved by an adaptive choice of k .