{
  "schema_version": 1,
  "title": "Optimal structure learning and conditional independence testing",
  "emoji": "🎯",
  "space_id": "snaykey/repro-optimal-structure-learning-and-conditional-independence-testing",
  "paper": {
    "openreview_id": "uurjpxrLc5"
  },
  "tags": [
    "icml2026-repro",
    "paper-uurjpxrLc5"
  ],
  "updated_at": "2026-07-24T09:39:47+00:00",
  "root": {
    "slug": "index",
    "title": "Optimal structure learning and conditional independence testing",
    "file": "pages/index.md",
    "children": [
      {
        "slug": "c1-optimal-sample-complexity-poly-forest",
        "title": "Theorem 3.1 establishes that when conditional independence (CI) testing achieves minimax separation radius c asymptotic to n^(-1/alpha), the corresponding poly-forest structure learning problem achieves optimal sample complexity n asymptotic to (log d)/c^alpha, implementable via the PC-tree algorithm (Theorem 3.1).",
        "file": "pages/c1-optimal-sample-complexity-poly-forest/page.md",
        "children": []
      },
      {
        "slug": "c2-sample-complexity-bernoulli-gaussian",
        "title": "For Bernoulli and Gaussian graphical models, the optimal sample complexity for structure learning is n asymptotic to (log d)/c^2 (Theorem 4.1, Theorem 4.2).",
        "file": "pages/c2-sample-complexity-bernoulli-gaussian/page.md",
        "children": []
      },
      {
        "slug": "c3-sample-complexity-nonparametric",
        "title": "For nonparametric graphical models with smoothness parameter s, the optimal sample complexity is n asymptotic to (log d)/c^((5s+2)/(2s)) (Theorem 5.1).",
        "file": "pages/c3-sample-complexity-nonparametric/page.md",
        "children": []
      },
      {
        "slug": "c4-pc-tree-algorithm-complexity",
        "title": "Proposes the PC-tree algorithm (Algorithm 1), a modification of the classical PC algorithm that tests only marginal and single-variable conditioning independence relations, requiring roughly d^3 tests instead of an exponential number, while remaining minimax optimal (Algorithm 1, Section 3).",
        "file": "pages/c4-pc-tree-algorithm-complexity/page.md",
        "children": []
      },
      {
        "slug": "executive-summary",
        "title": "Executive summary",
        "file": "pages/executive-summary/page.md",
        "children": []
      },
      {
        "slug": "conclusion",
        "title": "Conclusion",
        "file": "pages/conclusion/page.md",
        "children": []
      }
    ]
  },
  "agent_view_tokens": 716,
  "revision": "1784885987027359400"
}