---
res:
  bibo_abstract:
  - "In a mixed generalized linear model, the goal is to learn multiple signals from
    unlabeled observations: each sample comes from exactly one signal, but it is not
    known which one. We consider the prototypical problem of estimating two statistically
    independent signals in a mixed generalized linear model with Gaussian covariates.
    Spectral methods are a popular class of estimators which output the top two eigenvectors
    of a suitable data-dependent matrix. However, despite the wide applicability,
    their design is still obtained via heuristic considerations, and the number of
    samples \U0001D45B needed to guarantee recovery is superlinear in the signal dimension
    \U0001D451. In this paper, we develop exact asymptotics on spectral methods in
    the challenging proportional regime in which \U0001D45B,\U0001D451 grow large
    and their ratio converges to a finite constant. This allows us optimize the design
    of the spectral method, and combine it with a simple linear estimator, to minimize
    the estimation error. Our characterization exploits a mix of tools from random
    matrices, free probability, and the theory of approximate message passing algorithms.
    Numerical simulations for mixed linear regression and phase retrieval demonstrate
    the advantage enabled by our analysis over existing designs of spectral methods.@eng"
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Yihan
      foaf_name: Zhang, Yihan
      foaf_surname: Zhang
  - foaf_Person:
      foaf_givenName: Marco
      foaf_name: Mondelli, Marco
      foaf_surname: Mondelli
      foaf_workInfoHomepage: http://www.librecat.org/personId=27EB676C-8706-11E9-9510-7717E6697425
    orcid: 0000-0002-3242-7020
  - foaf_Person:
      foaf_givenName: Ramji
      foaf_name: Venkataramanan, Ramji
      foaf_surname: Venkataramanan
  bibo_doi: 10.1137/24m1702854
  bibo_issue: '2'
  bibo_volume: 8
  dct_date: 2026^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/2577-0187
  dct_language: eng
  dct_publisher: Society for Industrial & Applied Mathematics@
  dct_subject:
  - spectral estimator
  - generalized linear models
  - mixed regression
  - high-dimensional asymptotics
  - random matrix theory
  - approximate message passing (AMP)
  dct_title: Precise asymptotics for spectral methods in mixed generalized linear
    models@
...