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  4. Spectral Phase Transition and Optimal PCA in Block-Structured Spiked Models
 
conference paper

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

Mergny, Pierre  
•
Ko, Justin
•
Krzakala, Florent  
2024
Proceedings of the 41st International Conference on Machine Learning
The Forty-first International Conference on Machine Learning

We discuss the inhomogeneous Wigner spike 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 (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.

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Type
conference paper
Author(s)
Mergny, Pierre  

EPFL

Ko, Justin

University of Waterloo

Krzakala, Florent  

EPFL

Date Issued

2024

Published in
Proceedings of the 41st International Conference on Machine Learning
Series title/Series vol.

Proceedings of Machine Learning Research; 235

ISSN (of the series)

2640-3498

Start page

35470

End page

35491

URL

Link to the paper

https://proceedings.mlr.press/v235/mergny24a.html
Editorial or Peer reviewed

REVIEWED

Written at

EPFL

EPFL units
IDEPHICS2  
Event nameEvent acronymEvent placeEvent date
The Forty-first International Conference on Machine Learning

ICML

Vienna, Austria

2024-07-21 - 2024-07-27

Available on Infoscience
September 5, 2024
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/240978
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