Estimating differential entropy using recursive copula split

An algorithm for estimating the entropy of a continuous random variable. Uses recursive splitting of the copula.

A method for estimating the Shannon differential entropy of multidimensional random variables using independent samples. The method is based on decomposing the distribution into a product of the marginal distributions and the joint dependency, also known as the copula. The entropy of marginals is estimated using one-dimensional methods.The entropy of the copula, which always has a compact support, is estimated recursively by splitting the data along statistically dependent dimensions.

The method can be applied both for distributions with compact and non-compact support. See Ariel and Louzoun, arXiv:1911.06204 for details.