On data-driven histogram-based estimation for mutual information
The problem of mutual information (MI) estimation based on data-dependent partition is addressed in this work. Sufficient conditions are stipulated on a histogram-based construction to guarantee a strong consistent estimate for the MI. The practical implications of this result are in the specification of a range of design parameters for two data-driven histogram-based approaches — statistically equivalent blocks and tree-structure vector quantizations — to yield density-free strongly consistent estimates for the MI.