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"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": []
}
]
},
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"revision": "1784885987027359400"
} |