mlsanityData to 7 Oct 2026

Spectral Phase Transition and Optimal PCA in Block-Structured Spiked models

arXiv 2403.03695 ↗First posted 6 Mar 2024stat.ML cond-mat.dis-nn cs.LGcited by 4

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Abstract (arXiv)

We discuss the inhomogeneous spiked Wigner model, a theoretical framework recently introduced to study structured noise in various learning scenarios, through the prism of random matrix theory, with a specific focus on its spectral properties. Our primary objective is to find an optimal spectral method and to extend the celebrated citeBBP (BBP) phase transition criterion -- well-known in the homogeneous case -- to our inhomogeneous, block-structured, Wigner model. We provide a thorough rigorous analysis of a transformed matrix and show that the transition for the appearance of 1) an outlier outside the bulk of the limiting spectral distribution and 2) a positive overlap between the associated eigenvector and the signal, occurs precisely at the optimal threshold, making the proposed spectral method optimal within the class of iterative methods for the inhomogeneous Wigner problem.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 17 of its 65 references that are in the map. First posted on arXiv 6 Mar 2024.

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17 of 65 references.

References · 17

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5 more
  1. 2018Rank-one matrix estimation: analysis of algorithmic and information theoretic limits by the spatial coupling methodcited by 11
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Cited by year

Citing papers per year: 2024: 2; 2025: 2.

4 papers.

  1. 2024Matrix Denoising with Doubly Heteroscedastic Noise: Fundamental Limits and Optimal Spectral Methodscited by 5
  2. 2024Optimal thresholds and algorithms for a model of multi-modal learning in high dimensionscited by 4
  3. 2025Sparse corruption in low-rank matrix inference: the PCA benchmarkcited by 1
  4. 2025Implicitly Normalized Online PCA: A Regularized Algorithm with Exact High-Dimensional Dynamicscited by 0