A near-optimal (minimax) tree-structured partition for mutual information estimation

A novel histogram-based mutual information estimator using data-driven tree-structured partitions (TSP) is presented in this work. The TSP is the solution of a complexity regularized empirical information maximization (EIM) criterion, with the objective to find a good tradeoff between the known estimation and approximation errors. We show that this solution is density-free strongly consistent and, furthermore, it provides a near-optimal balance between the mentioned variance-bias errors.