| { |
| "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" |
| } |
|
|
