{
 "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": []
   }
  ]
 }
}