Non-Parametric Mutual Information Estimation with Vine Copulas

Sigurd Holmsen, Berit Omli Øksnes, Ingrid Hobæk Haff, Sylvia Richardson, Ali Ramezani-Kebrya

We introduce VINE: a non-parametric mutual information (MI) estimator based on simplified D-vine copulas. Approximating the joint density with a simplified D-vine allows the density ratio to simplify to a product of pair copulas, which we can estimate non-parametrically. This structural simplification yields VINE, a flexible and computationally efficient MI estimator. We compare VINE against SotA neural MI estimators on a range of datasets, both under settings where the simplified D-vine assumption holds and where it is violated, demonstrating competitive accuracy at a lower computational cost for low- to medium-dimensional datasets.