---
res:
  bibo_abstract:
  - "We study the problem of recovering an unknown signal \U0001D465\U0001D465 given
    measurements obtained from a generalized linear model with a Gaussian sensing
    matrix. Two popular solutions are based on a linear estimator \U0001D465\U0001D465^L
    and a spectral estimator \U0001D465\U0001D465^s. The former is a data-dependent
    linear combination of the columns of the measurement matrix, and its analysis
    is quite simple. The latter is the principal eigenvector of a data-dependent matrix,
    and a recent line of work has studied its performance. In this paper, we show
    how to optimally combine \U0001D465\U0001D465^L and \U0001D465\U0001D465^s. At
    the heart of our analysis is the exact characterization of the empirical joint
    distribution of (\U0001D465\U0001D465,\U0001D465\U0001D465^L,\U0001D465\U0001D465^s)
    in the high-dimensional limit. This allows us to compute the Bayes-optimal combination
    of \U0001D465\U0001D465^L and \U0001D465\U0001D465^s, given the limiting distribution
    of the signal \U0001D465\U0001D465. When the distribution of the signal is Gaussian,
    then the Bayes-optimal combination has the form \U0001D703\U0001D465\U0001D465^L+\U0001D465\U0001D465^s
    and we derive the optimal combination coefficient. In order to establish the limiting
    distribution of (\U0001D465\U0001D465,\U0001D465\U0001D465^L,\U0001D465\U0001D465^s),
    we design and analyze an approximate message passing algorithm whose iterates
    give \U0001D465\U0001D465^L and approach \U0001D465\U0001D465^s. Numerical simulations
    demonstrate the improvement of the proposed combination with respect to the two
    methods considered separately.@eng"
  bibo_authorlist:
  - 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: Christos
      foaf_name: Thrampoulidis, Christos
      foaf_surname: Thrampoulidis
  - foaf_Person:
      foaf_givenName: Ramji
      foaf_name: Venkataramanan, Ramji
      foaf_surname: Venkataramanan
  bibo_doi: 10.1007/s10208-021-09531-x
  bibo_issue: '5'
  bibo_volume: 22
  dct_date: 2022^xs_gYear
  dct_identifier:
  - UT:000685721000001
  dct_isPartOf:
  - http://id.crossref.org/issn/1615-3375
  - http://id.crossref.org/issn/1615-3383
  dct_language: eng
  dct_publisher: Springer@
  dct_subject:
  - Applied Mathematics
  - Computational Theory and Mathematics
  - Computational Mathematics
  - Analysis
  dct_title: Optimal combination of linear and spectral estimators for generalized
    linear models@
...