Add ShaplEIG: Bayesian experimental design approximator

[david-rundel]

ShaplEIG fits a Gaussian process surrogate with a weighted Hamming product kernel on queried coalition values and sequentially selects coalitions by maximizing the closed-form expected information gain about the Shapley values. The Shapley structure is handled via elementary-symmetric-polynomial identities of the kernel's generating polynomials, so the 2^n coalition space is never enumerated.

• new optional extra 'shapleig' (torch/gpytorch/botorch/linear_operator) with lazy import and an informative placeholder when not installed
• shapiq/approximator/shapleig/: approximator + flat Hamming GP surrogate + self-contained ESP math core (controlled copy of the validated reference implementation, kept in sync)
• order-1 SV InteractionValues output (min_order=0, baseline = empty coalition value); SV-variance return left as a commented scaffold until InteractionValues supports uncertainty information
• tqdm progress bar over the BED iterations
• registered in SV_APPROXIMATORS and the public API; unit tests covering output format, determinism, and convergence to ExactComputer ground truth

Motivation and Context

This PR adds ShaplEIG, an approximator for Shapley values based on Bayesian experimental design (BED), accompanying the paper "ShaplEIG: Bayesian Experimental Design for Shapley Value Estimation" (Rundel et al., 2026).

The scope was pre-agreed with @mmschlk and @Advueu963: a black-box, end-to-end approximator in shapiq/approximator/shapleig/ behind a new optional dependency group shapleig.

Open questions for the maintainers:

• The shapleig extra is pinned to the exact versions used for the published experiments
  (torch==2.9.1, gpytorch==1.14, botorch==0.14.0, linear_operator==0.6). Is this ok?
• The surrogate posterior also provides the marginal SV variances; the code contains a commented
  scaffold to expose them via an approximate_with_variance once InteractionValues supports
  uncertainty information (future work, as discussed).

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Public API Changes

• No Public API changes

• Yes, Public API changes (Details below)

• New public class shapiq.ShaplEIG (= shapiq.approximator.shapleig.ShaplEIG), registered in
  SV_APPROXIMATORS.

• New optional dependency group shapleig in pyproject.toml.

• No changes to any existing API. import shapiq works without the extra installed (the optional
  dependencies are imported in ShaplEIG.__init__, which raises an ImportError pointing to pip install 'shapiq[shapleig]' when they are missing).

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How Has This Been Tested?

• New unit tests in tests/shapiq/tests_unit/tests_approximators/test_approximator_shapleig.py:
  output format (InteractionValues, order 1, min_order=0, baseline = empty-coalition value),
  determinism under random_state, convergence to ExactComputer ground truth with growing budget,
  budget/candidate-set validation, sampled-candidate-subset and warmstart configurations.
• Verified bit-identical against the validated reference implementation of the paper on the
  same game/seed/protocol (default and warmstart configurations).
• Full local unit suite passes (852 passed; the only failures are pre-existing [spex] tests
  caused by the sparse extra not being installed locally, identical on main).

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Checklist

• The changes have been tested locally.
• Documentation has been updated (if the public API or usage changes). (Not actively. Does the API reference pick
  ShaplEIG up via the shapiq.approximator autosummary?)
• An entry has been added to CHANGELOG.md (if relevant for users).
• The code follows the project's style guidelines.
• I have considered the impact of these changes on the public API.

---

[codecov]

Codecov Report

❌ Patch coverage is 88.93805% with 50 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
src/shapiq/approximator/shapleig/shapleig.py	82.23%	27 Missing ⚠️
src/shapiq/approximator/shapleig/_shapley_math.py	92.46%	18 Missing ⚠️
src/shapiq/approximator/shapleig/_surrogate.py	91.37%	5 Missing ⚠️

📢 Thoughts on this report? Let us know!