Figure 2. Comparison of MIC to Existing Methods.

(A) Scores given to various noiseless functional relationships by several different statistics (8, 12, 14, 19). Maximal scores in each column are accentuated. (B-F) The MIC, Spearman correlation coefficient, mutual information (Kraskov et al. estimator), maximal correlation (via ACE), and the principal curve-based CorGC dependence measure, respectively, of 27 different functional relationships with independent uniform vertical noise added, as the R² value of the data relative to the noiseless function varies. Each shape/color corresponds to a different combination of function type and sample size. In each plot, pairs of thumbnails show relationships that received identical scores; for data exploration, we would like these pairs to have similar noise levels. For a list of the functions and sample sizes in these graphs as well as versions with other statistics, sample sizes, and noise models, see Figs. S3 and S4. (G) Performance of MIC on associations not well modeled by a function, as noise level varies. For the performance of other statistics, see Figs. S5 and S6.