{
  "schema_version": "1.0",
  "title": "Mean-Shift PCA by Knockoff Mean",
  "emoji": "📐",
  "space_id": "snaykey/repro-simulcost",
  "paper": {
    "arxiv_id": "2605.25460",
    "openreview_id": "ISNSiAC3n1"
  },
  "tags": [
    "icml2026-repro",
    "paper-ISNSiAC3n1"
  ],
  "updated_at": "2026-07-29T15:36:24.484193+00:00",
  "root": {
    "slug": "index",
    "title": "Mean-Shift PCA by Knockoff Mean",
    "children": [
      {
        "slug": "executive-summary",
        "title": "Executive summary",
        "children": [],
        "file": "pages/executive-summary/page.md"
      },
      {
        "slug": "claim-1-theorem-3-5-spectral-separation",
        "title": "Theorem 3.5 proves that mean-shift-induced spiked eigenvalues (set Λ_A) are spectrally separable from the covariance-induced spikes (set Λ_P) in high dimensions, using tools from Random Matrix Theory under the additive low-rank perturbation model (Section 3, Theorem 3.5).",
        "children": [],
        "file": "pages/claim-1-theorem-3-5-spectral-separation/page.md"
      },
      {
        "slug": "claim-2-theorem-3-11-eigenspace-invariance",
        "title": "Theorem 3.11 (Eigenspace Invariance) shows that the eigenspace of the uncontaminated sample covariance matrix remains asymptotically invariant under mean-shift mixture contamination, regardless of the mixture weight π (Section 3, Theorem 3.11).",
        "children": [],
        "file": "pages/claim-2-theorem-3-11-eigenspace-invariance/page.md"
      },
      {
        "slug": "claim-3-algorithm-1-knockoff-mean",
        "title": "The proposed two-stage Mean-Shift PCA (MS-PCA, Algorithm 1) deliberately injects an artificial knockoff mean-shift perturbation A'_n = m'γ'^T with mixture weight π' (e.g., π'=0.5 or π'=1) and threshold ϵ=Cn^(-1/2) to identify and remove the mean-shift eigenvalues while leaving covariance-induced eigenvalues invariant (Section 2, Algorithm 1).",
        "children": [],
        "file": "pages/claim-3-algorithm-1-knockoff-mean/page.md"
      },
      {
        "slug": "claim-4-eigenvalue-fluctuation-orders",
        "title": "Both mean-shift-induced spikes and covariance-induced spikes fluctuate at order O(n^-1/2), except the largest eigenvalue at the spectral edge which fluctuates at order O(n^-2/3), as used to set the matching threshold in the algorithm (Section 2, citing Theorem 2.19/2.16/2.15 of prior RMT results).",
        "children": [],
        "file": "pages/claim-4-eigenvalue-fluctuation-orders/page.md"
      },
      {
        "slug": "claim-5-figure-2-high-dimensional-recovery",
        "title": "Section 4 numerical experiments show that existing Robust PCA methods fail to recover the true principal component even with only 5% outlier proportion when the aspect ratio d/n does not vanish (e.g., d/n=1), whereas MS-PCA consistently recovers it (Figure 2, Section 4).",
        "children": [],
        "file": "pages/claim-5-figure-2-high-dimensional-recovery/page.md"
      },
      {
        "slug": "conclusion",
        "title": "Conclusion",
        "children": [],
        "file": "pages/conclusion/page.md"
      }
    ],
    "file": "pages/index.md"
  },
  "revision": 1
}