Fig 3. Equitability and convergence of $\widehat{\mathbf{\text{A}}}$.

Top: For functions of 2 variables, $\widehat{A}$ is approximately equitable, as demonstrated with 16 example functions, with N = 1000. Each function is marked with a different color. $\widehat{A}$ (left) is closer to the classical R² than MIC (right), especially for associations near independence. Bottom: Estimates of association from $\widehat{A}$ (left) and MIC (right) as sample size (N) increases for three different relationships: a noiseless circle (red), a bivariate normal distribution with expected R² = 0.5 (green), and independent noise (blue). MIC converges very slowly.