Top pick: O-information + permutation null (hoi (BSD-3) โ bias-centered shuffle null; naive |ฮฉ|โฅ0.5 flag dropped). Fills the gap: Synergy (higher-order) โ de-scoped to a cheap permutation-null watch 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 |
|---|---|---|---|---|---|---|---|
| Continuous-BROJA (Pakman 2021) | Author repo (NeurIPS 2021) | varies | Python | โ ๏ธ | high (VAE) | yes | โ |
| IDTxl | IDTxl | GPLv3 | Python | โ | varies | yes | โ |
| JIDT (KSG + many estimators) | jidt | GPLv3 | Java+Python | โ | varies | yes | โ |
| BROJA-2PID | BROJA_2PID | MIT-compatible | Python | โ | cone programming | no | โ |
| O-information | HOI | BSD-3 | Python | โ | O(N) Gaussian; O(N log N) k-NN | no | โ |
| dit (PID family) | dit | BSD-3 | Python | โ | varies | no | โ |