Top pick: GCM / RCoT (GeneralisedCovarianceMeasure (CRAN) ยท RCIT/RCoT (causal-learn)). Fills the gap: Conditional redundancy (CODEC SKIPPED โ inert on substrate + no faithful FOSS null) 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 |
|---|---|---|---|---|---|---|---|
| CMIknn | tigramite.independence_tests.CMIknn | GPLv3 | Python | โ | O(N log N d) | yes | โ |
| CODEC/FOCI (Azadkia-Chatterjee) | FOCI | GPL | R | โ | O(N log N) per eval | no | โ |
| Generalised Covariance Measure (GCM) | GeneralisedCovarianceMeasure / pywhy-dodiscover | GPL-3 / BSD-3 | R / Python | โ | O(N) โ two regressions + scalar covariance test | no | โ |
| IDTxl | IDTxl | GPLv3 | Python | โ | varies | yes | โ |
| LPCMCI | tigramite | GPLv3 | Python | โ | higher than PCMCI | yes | โ |
| PCMCI / PCMCI+ | tigramite | GPLv3 | Python | โ | O(N V^2 tau_max k_test) | yes | โ |
| RCoT / RCIT (randomized conditional) | causal-learn (RCIT) / ericstrobl-RCIT | MIT / GPL-3 | Python / R | โ | O(N) โ random Fourier features (linear-time KCI approx) | yes | โ |
| CODEC/FOCI โ Python | xicorpy.select_features_using_foci | MIT | Python | โ | ? | โ | |
| Graphical Lasso | sklearn.covariance.GraphicalLasso | Apache-2 | Python | โ | O(N^3) per iter | yes | โ |
| CDCIT (diffusion-based CI) | CDCIT | unverified | Python | โ ๏ธ | high (diffusion training) | yes | โ |
| PMIME | PMIME-and-TE | no LICENSE โ commercial use needs author contact | MATLAB+Python | โ ๏ธ | O(N K L log N) | yes | โ |