[flyingdoubleG]

Summary

SHAPIQ and SVARMIQ (MonteCarlo) estimate the chaining interaction index ("CHII") wrongly, even with a budget of all 2**n coalitions. Their CHII estimates are off by tens on a small game, including at order 1, where CHII equals the Shapley value.

MonteCarlo._log_chii_weight uses s / t as the weight of the discrete derivatives. s / |T| is the coefficient of CHII's Möbius representation, CHII(S) = sum_{T >= S} s / |T| * m(T). As a cardinal interaction index, CHII(S) = sum_{T ⊆ N \ S} p(t) Δ_S v(T), the weight is

p(t) = s * (s + t - 1)! * (n - s - t)! / n!

This weight is nonzero for the empty coalition. Summed over the coalitions containing R, it gives back s / (s + |R|). For example, with s = 1 and R = ∅, sum_t C(n-1, t) t! (n-1-t)! / n! = 1. ExactComputer already computes CHII correctly: it matches the Möbius formula and equals the SV at order 1.

Reproduction

All approximators run at budget 2**6 on a random game with order 1–3 interactions, compared with ExactComputer. Before the change, the only combinations far from exact apart from the sampling estimators were:

SHAPIQ   CHII order=1  max|err|=2.56e+01      after: 8.9e-16
SHAPIQ   CHII order=2  max|err|=3.58e+01      after: 8.9e-16
SHAPIQ   CHII order=3  max|err|=3.58e+01      after: 1.8e-15
SVARMIQ  CHII (same)

Change

• _log_chii_weight now returns log s + gammaln(s + t) + gammaln(n - s - t + 1) - gammaln(n + 1).
• New test test_full_budget_matches_exact: the full-budget MonteCarlo estimates of SII, BII, STII and CHII at orders 1–3 equal ExactComputer on a SOUM game. The existing test_approximate only checks that the estimate is nonzero. The CHII cases fail before the change; the others pass both before and after.

Testing

• tests/shapiq/tests_unit/tests_approximators: 623 passed. I skipped the tests that need the sparse/xgboost extras. OddSHAP has 30 failures in my environment, which uses a stubbed tree C extension because I have no MSVC; the same 30 fail on main.
• ruff check and ruff format (0.15.5, as in uv.lock) are clean.

The CHANGELOG has an entry under Development.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.

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[Advueu963]

Thanks for spotting this! I have adjusted the comments and would merge this once the tests run through nicely.

[Advueu963]

Checked by hand and with unit tests.