Top pick: Chatterjee ฮพโ (xicorpy (MIT) โ VALIDATED (Selection-partial)). Fills the gap: Non-linear redundancy (ฮพ: S1/S2/S3/S5 PASS; value-add pending S4) โ which the production baseline (Pearson + Spearman + h_norm + Tier-2 MI-vs-target) cannot detect.
Lane = how usable the metric is today. Top lane = production-baseline duplicates (Pearson, Spearman). Below = permissive FOSS / GPL / unmaintained / code-released-but-not-packaged / no-FOSS. Per-circle text = first 3 letters of language (Pyt / R / Jav).
| Metric | Library | License | Lang | Maint | Complexity | Param-free? | URL |
|---|---|---|---|---|---|---|---|
| Robust dCor (Leyder 2024) | Author code (not packaged) | varies | R | โ ๏ธ | O(N^2) | no | โ |
| Bergsma-Dassios tau-star | TauStar | GPL | R | โ | O(N log N) | no | โ |
| Chatterjee xi โ R | XICOR | GPL | R | โ | O(N log N) | no | โ |
| Distance Correlation (dCor) โ R | energy | GPL | R | โ | O(N^2) | no | โ |
| Distance Multivariance | multivariance | GPL | R | โ | O(N^2) per cdm | no | โ |
| HHG | HHG | GPL | R | โ | O(N^2 log N) per perm | yes | โ |
| IDTxl | IDTxl | GPLv3 | Python | โ | varies | yes | โ |
| JIDT (KSG + many estimators) | jidt | GPLv3 | Java+Python | โ | varies | yes | โ |
| MIC / MICe / TIC | minepy/mictools | GPL | Python+C | โ | polynomial; MICe efficient | yes | โ |
| Schweizer-Wolff sigma | copBasic | GPL | R | โ | O(N^2) | no | โ |
| dHSIC | dHSIC | GPL | R | โ | O(N^2 d) | yes | โ |
| Chatterjee xi | xicorpy | MIT | Python | โ | O(N log N) | no | โ |
| Copula Entropy | copent | MIT | Python | โ | O(N log N) | no | โ |
| Distance Correlation (dCor) | dcor | MIT | Python | โ | O(N^2) naive; O(N log N) univariate Huo-Szekely | no | โ |
| HSIC | hyppo.independence.Hsic | Apache-2 | Python | โ | O(N^2); Nystrom sub-quadratic | yes | โ |
| HSIC-Lasso | pyHSICLasso | MIT | Python | โ | O(d N^2) memory vanilla | yes | โ |
| Hoeffding D | independence | MIT | R | โ | O(N log N) | no | โ |
| KSG MI estimator | infomeasure | MIT | Python | โ | O(N log N) | yes | โ |
| Kendall tau | scipy.stats.kendalltau | BSD-3 | Python | โ | O(N log N) | no | โ |
| MINE (neural MI) | MINE | MIT | Python | โ | O(N epochs params) | yes | โ |
| Sliced Wasserstein primitives | POT | MIT | Python | โ | O(N log N d L) | yes | โ |
| Tail dependence (lambda_U, lambda_L) | pycop | MIT | Python | โ | O(N) | yes | โ |
| CLUB (MI upper bound) | CLUB | MIT | Python | โ ๏ธ | O(N params) | yes | โ |
| DiPMInd | not released | n/a | n/a | โ ๏ธ | O(N^2) | yes | โ |
| Lin-Han boosted xi | On-boosting-the-power-of-Chatterjee-s-rank-correlation | unknown | Python | โ ๏ธ | O(N log N) | yes | โ |
| Pearson r | scipy.stats.pearsonr | BSD-3 | Python | โ | O(N) | no | โ |
| Spearman rho | scipy.stats.spearmanr | BSD-3 | Python | โ | O(N log N) | no | โ |