{
  "schema_version": 1,
  "title": "Repro: Exactly Computing do-Shapley Values",
  "emoji": "🧮",
  "space_id": "snaykey/repro-do-shapley",
  "paper": {
    "openreview_id": "Peim0KY6ty"
  },
  "tags": [
    "icml2026-repro",
    "paper-Peim0KY6ty"
  ],
  "updated_at": null,
  "root": {
    "slug": "index",
    "title": "Repro: 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-exact-computation",
        "title": "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-exact-computation/page.md",
        "children": []
      },
      {
        "slug": "claim-2-identifiability",
        "title": "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-identifiability/page.md",
        "children": []
      },
      {
        "slug": "claim-3-lemma-31",
        "title": "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-31/page.md",
        "children": []
      },
      {
        "slug": "claim-4-boundary-sampling",
        "title": "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-boundary-sampling/page.md",
        "children": []
      },
      {
        "slug": "claim-5-phase-transition",
        "title": "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-phase-transition/page.md",
        "children": []
      },
      {
        "slug": "claim-6-sparsity-scaling",
        "title": "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-sparsity-scaling/page.md",
        "children": []
      },
      {
        "slug": "conclusion",
        "title": "Conclusion",
        "file": "pages/conclusion/page.md",
        "children": []
      }
    ]
  }
}