{
  "schema_version": 1,
  "title": "Reproduction: Theoretical Investigation on Inductive Bias of Isolation Forest",
  "emoji": "🌲",
  "space_id": "SabaPivot/repro-isolation-forest-inductive-bias",
  "paper": {
    "arxiv_id": "2505.12825",
    "openreview_id": "J0y3sNbo9G"
  },
  "tags": [
    "icml2026-repro",
    "paper-J0y3sNbo9G"
  ],
  "updated_at": "2026-07-29T04:50:27.940942+00:00",
  "root": {
    "slug": "index",
    "title": "Reproduction: Theoretical Investigation on Inductive Bias of Isolation Forest",
    "file": "pages/index.md",
    "children": [
      {
        "slug": "executive-summary",
        "title": "Executive summary",
        "file": "pages/executive-summary/page.md",
        "children": []
      },
      {
        "slug": "claim-1-expected-depth-random-walk",
        "title": "Claim 1: Isolation Forest's expected depth function is derived in closed form by modelling the iTree growth process as a random walk with transition probabilities based on point spacing (Theorem 3.5).",
        "file": "pages/claim-1-expected-depth-random-walk/page.md",
        "children": []
      },
      {
        "slug": "claim-2-marginal-single-anomaly",
        "title": "Claim 2: For marginal single anomalies, Isolation Forest's detection threshold scales as U·κ (data-dependent), while k-NN requires separation greater than U+(k−1)δ/2 (parameter-dependent on k).",
        "file": "pages/claim-2-marginal-single-anomaly/page.md",
        "children": []
      },
      {
        "slug": "claim-3-central-anomaly-threshold",
        "title": "Claim 3: For central single anomalies, Isolation Forest's decision threshold is Θ(√(n₀κ)) versus k-NN's Θ(kδ), demonstrating iForest's lower sensitivity to centrally-located anomalies (Theorems 4.6–4.7, Table 2).",
        "file": "pages/claim-3-central-anomaly-threshold/page.md",
        "children": []
      },
      {
        "slug": "claim-4-marginal-clustered-anomalies",
        "title": "Claim 4: For marginal clustered anomalies of size n₁, Isolation Forest requires separation of order Θ(n₁²κ) while k-NN requires Θ(kδ) under the constraint ω(n₁) ≤ k ≤ o(n₀) (Theorems 4.8–4.9).",
        "file": "pages/claim-4-marginal-clustered-anomalies/page.md",
        "children": []
      },
      {
        "slug": "claim-5-depth-convergence-with-trees",
        "title": "Claim 5: Empirical mean-squared error between empirical and theoretical expected depths decreases as the number of trees increases, confirming the concentration property of Proposition 3.1 (Figure 3).",
        "file": "pages/claim-5-depth-convergence-with-trees/page.md",
        "children": []
      },
      {
        "slug": "claim-6-openml-assumption-audit",
        "title": "Claim 6: Across OpenML benchmark datasets, 930,738 of 930,751 tested dimensions satisfy the condition κ ≥ √(n+3) required for the theoretical analysis (Section 4, Assumption 4.2).",
        "file": "pages/claim-6-openml-assumption-audit/page.md",
        "children": []
      },
      {
        "slug": "claim-7-supporting-density-and-endpoint-geometry",
        "title": "Supporting evidence: iForest scores points using density and distance to endpoints, unlike k-NN",
        "file": "pages/claim-7-supporting-density-and-endpoint-geometry/page.md",
        "children": []
      },
      {
        "slug": "conclusion",
        "title": "Conclusion",
        "file": "pages/conclusion/page.md",
        "children": []
      }
    ]
  },
  "agent_view_tokens": 3500,
  "revision": "20260719-isolation-forest-inductive-bias-v1"
}