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  "title": "Reproduction: Exactly Computing do-Shapley Values",
  "emoji": "🎯",
  "space_id": "amkkk/repro-exactly-computing-do-shapley-values",
  "paper": {
    "arxiv_id": "2602.07203"
  },
  "tags": [
    "icml2026-repro",
    "paper-Peim0KY6ty"
  ],
  "updated_at": "2026-07-23T01:08:28+00:00",
  "root": {
    "slug": "index",
    "title": "Reproduction: Exactly Computing do-Shapley Values",
    "file": "pages/index.md",
    "children": [
      {
        "slug": "executive-summary",
        "title": "Executive summary",
        "file": "pages/executive-summary/page.md",
        "children": []
      },
      {
        "slug": "claim-1-do-shapley-values-can-be-computed-exactly-in-o-r-d-e-t-time-where-r-is-the-number-of-irreducible-sets-d-the-number-of-dimensions-e-the-number-of-edges-and-t-the-value-function-evaluation-time-versus-the-naive-2-d-complexity-section-3",
        "title": "Claim 1: Do-Shapley values can be computed exactly in O(r(d+e+T)) time, where r is the number of irreducible sets, d the number of dimensions, e the number of edges, and T the value-function evaluation time, versus the naive 2^d complexity (Section 3).",
        "file": "pages/claim-1-do-shapley-values-can-be-computed-exactly-in-o-r-d-e-t-time-where-r-is-the-number-of-irreducible-sets-d-the-number-of-dimensions-e-the-number-of-edges-and-t-the-value-function-evaluation-time-versus-the-naive-2-d-complexity-section-3/page.md",
        "children": []
      },
      {
        "slug": "claim-2-theorem-5-1-shows-the-do-shapley-value-phi-i-is-identifiable-if-and-only-if-nu-j-is-identifiable-for-all-j-in-d-reducing-identifiability-checks-from-r-coalitions-to-just-d-singleton-coalitions-theorem-5-1",
        "title": "Claim 2: Theorem 5.1 shows the do-Shapley value phi_i is identifiable if and only if nu({j}) is identifiable for all j in [d], reducing identifiability checks from r coalitions to just d singleton coalitions (Theorem 5.1).",
        "file": "pages/claim-2-theorem-5-1-shows-the-do-shapley-value-phi-i-is-identifiable-if-and-only-if-nu-j-is-identifiable-for-all-j-in-d-reducing-identifiability-checks-from-r-coalitions-to-just-d-singleton-coalitions-theorem-5-1/page.md",
        "children": []
      },
      {
        "slug": "claim-3-lemma-3-1-establishes-that-for-any-closed-set-with-a-basis-removing-any-basis-element-yields-another-closed-set-enabling-efficient-lattice-traversal-via-algorithm-2-lemma-3-1-algorithm-2",
        "title": "Claim 3: Lemma 3.1 establishes that for any closed set with a basis, removing any basis element yields another closed set, enabling efficient lattice traversal via Algorithm 2 (Lemma 3.1, Algorithm 2).",
        "file": "pages/claim-3-lemma-3-1-establishes-that-for-any-closed-set-with-a-basis-removing-any-basis-element-yields-another-closed-set-enabling-efficient-lattice-traversal-via-algorithm-2-lemma-3-1-algorithm-2/page.md",
        "children": []
      },
      {
        "slug": "claim-4-algorithm-3-boundary-sampling-guarantees-discovery-of-min-m-r-distinct-equivalence-classes-using-m-queries-running-in-o-m-d-d-e-time-section-on-estimator-performance-algorithm-3",
        "title": "Claim 4: Algorithm 3 (boundary sampling) guarantees discovery of min(m, r) distinct equivalence classes using m queries, running in O(m*d(d+e)) time (Section on estimator performance, Algorithm 3).",
        "file": "pages/claim-4-algorithm-3-boundary-sampling-guarantees-discovery-of-min-m-r-distinct-equivalence-classes-using-m-queries-running-in-o-m-d-d-e-time-section-on-estimator-performance-algorithm-3/page.md",
        "children": []
      },
      {
        "slug": "claim-5-the-doregressionmsr-estimator-consistently-outperforms-baseline-variants-and-exhibits-a-phase-transition-at-m-r-where-error-vanishes-to-machine-precision-while-structure-agnostic-methods-retain-variance-figure-5",
        "title": "Claim 5: The doRegressionMSR estimator consistently outperforms baseline variants and exhibits a phase transition at m=r, where error vanishes to machine precision while structure-agnostic methods retain variance (Figure 5).",
        "file": "pages/claim-5-the-doregressionmsr-estimator-consistently-outperforms-baseline-variants-and-exhibits-a-phase-transition-at-m-r-where-error-vanishes-to-machine-precision-while-structure-agnostic-methods-retain-variance-figure-5/page.md",
        "children": []
      },
      {
        "slug": "claim-6-real-world-causal-structures-tend-to-be-sparse-so-the-number-of-irreducible-sets-r-scales-between-the-exponential-worst-case-2-d-and-the-linear-lower-bound-d-figure-4",
        "title": "Claim 6: Real-world causal structures tend to be sparse, so the number of irreducible sets r scales between the exponential worst case 2^d and the linear lower bound d (Figure 4).",
        "file": "pages/claim-6-real-world-causal-structures-tend-to-be-sparse-so-the-number-of-irreducible-sets-r-scales-between-the-exponential-worst-case-2-d-and-the-linear-lower-bound-d-figure-4/page.md",
        "children": []
      },
      {
        "slug": "conclusion",
        "title": "Conclusion",
        "file": "pages/conclusion/page.md",
        "children": []
      }
    ]
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