Directed information per edge, and directed-information baselines

[Autoplectic]

Stacked on #2 (machines-layer).

Summary

Directed information per edge (infer_multiplex(directed_information=True))

• iie: the instantaneous information exchange of each pair, I[X_t : Y_t | both selected pasts and lagged parents], with a permutation p-value iie_pvalue. It is computed by the new infoflow.contemporaneous.instantaneous_exchange, which the lag-0 layer now reuses.
• di = weight[te] + iie: the bivariate decomposition of directed information into transfer entropy plus instantaneous exchange (Massey 1990; Amblard & Michel 2013). The docs note that with side information it is only approximate.
• model_di: the composed model's exact one-step directed information, added to the machine layer's exact flows.

Baselines and benchmark (validation/di_baselines.py, validation/di_benchmark.py, validation/run_di.sh)

• Pairwise directed information, with Benjamini-Hochberg over pairs.
• The directed information graph with in-degree at most K (Quinn, Kiyavash & Coleman 2015).
• Optimal causation entropy (Sun, Taylor & Bollt 2015).
• All are run on the same integer symbols and fixed lag grid as infoflow, on:
  • the tent ring (weak, moderate, and moderate at lag 1);
  • noisy ECA rules 90 and 110;
  • random 10-node VAR and logistic networks.
• The table is in docs/validation.rst. Highlights:
  • On rule 90 (pure synergy), oCSE and pairwise DI recover 2 of 12 edges. DIG and infoflow recover all 12, because they search parent sets and pairs.
  • DIG is exact on the automata because K equals their true in-degree, but it loses precision on the random networks (0.60 against infoflow's 0.93 on VAR).
  • Every method links the indirect paths on the coarse tent ring.

Tests

• tests/test_directed_information.py:
  • instantaneous coupling shows up as iie > 0 with di = te + iie;
  • without it, di is about te;
  • the result matches the lag-0 layer's statistic;
  • model_di equals model_te for a lagged channel.
• Full suite: 191 passed. ty and ruff are clean, and the docs build without warnings.

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