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"schema_version": 1,
"title": "Repro: Combinatorial Sparse PCA Beyond the Spiked Identity Model",
"emoji": "chart",
"space_id": "snaykey/repro-combinatorial-sparse-pca",
"paper": {
"openreview_id": "Kk5UZgkWFx"
},
"tags": [
"icml2026-repro",
"paper-Kk5UZgkWFx"
],
"updated_at": "2026-07-26T00:00:00+00:00",
"root": {
"slug": "index",
"title": "Repro: Combinatorial Sparse PCA Beyond the Spiked Identity Model",
"file": "pages/index.md",
"children": [
{
"slug": "executive-summary",
"title": "Executive summary",
"file": "pages/executive-summary/page.md",
"children": []
},
{
"slug": "claim-1-diagonal-thresholding-fails",
"title": "Diagonal thresholding provably fails on the general-covariance model (Model 2), failing to detect any true support element with probability at least 1/2 even with a Θ(1) eigenvalue gap (Lemma 1, Section 3).",
"file": "pages/claim-1-diagonal-thresholding-fails/page.md",
"children": []
},
{
"slug": "claim-2-covariance-thresholding-fails",
"title": "Covariance thresholding fails analogously, returning an estimate 𝐮 with sin²∠(𝐮,𝐯)=1 with probability at least 1/2 despite sufficient samples (Lemma 3, Section 3).",
"file": "pages/claim-2-covariance-thresholding-fails/page.md",
"children": []
},
{
"slug": "claim-3-greedy-recovers-at-most-one",
"title": "Greedy correlation-based selection recovers at most one true support coordinate under Model 2, even when seeded with a correct coordinate (Lemma 4, Section 3).",
"file": "pages/claim-3-greedy-recovers-at-most-one/page.md",
"children": []
},
{
"slug": "claim-4-rtpm-recovery-sample-complexity",
"title": "The proposed Restarted Truncated Power Method (RTPM) achieves ⟨𝐯,𝐮⟩² ≥ 9/10 with probability ≥ 1-δ under Model 2 using n = Ω(s² log(s) log(d/δ)) samples and O(nd²) runtime (Theorem 1, Section 4.1).",
"file": "pages/claim-4-rtpm-recovery-sample-complexity/page.md",
"children": []
},
{
"slug": "claim-5-deflation-barrier-dense-eigenvector",
"title": "Sparse k-PCA cannot be solved by deflation-based self-reduction to the single-component case, since deflated covariance matrices can have fully dense top eigenvectors (Lemma 11, Section 4.2).",
"file": "pages/claim-5-deflation-barrier-dense-eigenvector/page.md",
"children": []
},
{
"slug": "conclusion",
"title": "Conclusion",
"file": "pages/conclusion/page.md",
"children": []
}
]
}
} |