{
  "schema_version": "1.0",
  "title": "Reproduction: Finding Most Influential Sets",
  "emoji": "🔍",
  "space_id": "snaykey/repro-most-influential-sets",
  "paper": {
    "arxiv_id": "2606.05919",
    "openreview_id": "ghd0zmtpB9"
  },
  "tags": [
    "icml2026-repro",
    "paper-ghd0zmtpB9"
  ],
  "updated_at": "2026-07-29T12:00:00+00:00",
  "root": {
    "slug": "index",
    "title": "Reproduction: Finding Most Influential Sets",
    "children": [
      {
        "slug": "executive-summary",
        "title": "Executive summary",
        "children": []
      },
      {
        "slug": "claim-1-linear-fractional-reduction",
        "title": "The Most Influential Sets (MIS) problem for estimands with linear-fractional leave-set-out effects is reduced to a one-parameter sequence of top-k selections solved via Dinkelbach's method (Section 3.1, Algorithm 1)",
        "children": []
      },
      {
        "slug": "claim-2-theorem-1-complexity",
        "title": "Algorithm 1 costs O(n) per iteration and provably terminates in at most M+1 ratio updates, where M is the number of distinct achievable ratio values, returning a globally optimal set (Theorem 1)",
        "children": []
      },
      {
        "slug": "claim-3-theorem-2-consistency",
        "title": "Under a uniform-denominator and generated-score-stability assumption, the empirical selection objective uniformly approximates the oracle orthogonal-score objective with o_p(1) error, yielding selection consistency given a separation condition on the ratio gap (Theorem 2)",
        "children": []
      },
      {
        "slug": "claim-4-runtime-scale",
        "title": "At n=10^6 and k=10^5, the algorithm's median wall-clock runtime is below 200ms, converging in a median of three ratio-update iterations (Section 4.1.2)",
        "children": []
      },
      {
        "slug": "claim-5-algorithm-2-warmstart",
        "title": "A warm-start variant (Algorithm 2) traces the most influential set across k=1,...,K by initializing each successive top-k problem from the previous solution (Section 3.2)",
        "children": []
      },
      {
        "slug": "conclusion",
        "title": "Conclusion",
        "children": []
      }
    ]
  },
  "revision": 1
}