---
_id: '12480'
abstract:
- lang: eng
  text: 'We consider the problem of estimating a signal from measurements obtained
    via a generalized linear model. We focus on estimators based on approximate message
    passing (AMP), a family of iterative algorithms with many appealing features:
    the performance of AMP in the high-dimensional limit can be succinctly characterized
    under suitable model assumptions; AMP can also be tailored to the empirical distribution
    of the signal entries, and for a wide class of estimation problems, AMP is conjectured
    to be optimal among all polynomial-time algorithms. However, a major issue of
    AMP is that in many models (such as phase retrieval), it requires an initialization
    correlated with the ground-truth signal and independent from the measurement matrix.
    Assuming that such an initialization is available is typically not realistic.
    In this paper, we solve this problem by proposing an AMP algorithm initialized
    with a spectral estimator. With such an initialization, the standard AMP analysis
    fails since the spectral estimator depends in a complicated way on the design
    matrix. Our main contribution is a rigorous characterization of the performance
    of AMP with spectral initialization in the high-dimensional limit. The key technical
    idea is to define and analyze a two-phase artificial AMP algorithm that first
    produces the spectral estimator, and then closely approximates the iterates of
    the true AMP. We also provide numerical results that demonstrate the validity
    of the proposed approach.'
acknowledgement: "The authors would like to thank Andrea Montanari for helpful discussions.\r\nM
  Mondelli was partially supported by the 2019 Lopez-Loreta Prize. R Venkataramanan
  was partially supported by the Alan Turing Institute under the EPSRC Grant\r\nEP/N510129/1."
article_number: '114003'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Marco
  full_name: Mondelli, Marco
  id: 27EB676C-8706-11E9-9510-7717E6697425
  last_name: Mondelli
  orcid: 0000-0002-3242-7020
- first_name: Ramji
  full_name: Venkataramanan, Ramji
  last_name: Venkataramanan
citation:
  ama: 'Mondelli M, Venkataramanan R. Approximate message passing with spectral initialization
    for generalized linear models. <i>Journal of Statistical Mechanics: Theory and
    Experiment</i>. 2022;2022(11). doi:<a href="https://doi.org/10.1088/1742-5468/ac9828">10.1088/1742-5468/ac9828</a>'
  apa: 'Mondelli, M., &#38; Venkataramanan, R. (2022). Approximate message passing
    with spectral initialization for generalized linear models. <i>Journal of Statistical
    Mechanics: Theory and Experiment</i>. IOP Publishing. <a href="https://doi.org/10.1088/1742-5468/ac9828">https://doi.org/10.1088/1742-5468/ac9828</a>'
  chicago: 'Mondelli, Marco, and Ramji Venkataramanan. “Approximate Message Passing
    with Spectral Initialization for Generalized Linear Models.” <i>Journal of Statistical
    Mechanics: Theory and Experiment</i>. IOP Publishing, 2022. <a href="https://doi.org/10.1088/1742-5468/ac9828">https://doi.org/10.1088/1742-5468/ac9828</a>.'
  ieee: 'M. Mondelli and R. Venkataramanan, “Approximate message passing with spectral
    initialization for generalized linear models,” <i>Journal of Statistical Mechanics:
    Theory and Experiment</i>, vol. 2022, no. 11. IOP Publishing, 2022.'
  ista: 'Mondelli M, Venkataramanan R. 2022. Approximate message passing with spectral
    initialization for generalized linear models. Journal of Statistical Mechanics:
    Theory and Experiment. 2022(11), 114003.'
  mla: 'Mondelli, Marco, and Ramji Venkataramanan. “Approximate Message Passing with
    Spectral Initialization for Generalized Linear Models.” <i>Journal of Statistical
    Mechanics: Theory and Experiment</i>, vol. 2022, no. 11, 114003, IOP Publishing,
    2022, doi:<a href="https://doi.org/10.1088/1742-5468/ac9828">10.1088/1742-5468/ac9828</a>.'
  short: 'M. Mondelli, R. Venkataramanan, Journal of Statistical Mechanics: Theory
    and Experiment 2022 (2022).'
corr_author: '1'
date_created: 2023-02-02T08:31:57Z
date_published: 2022-11-24T00:00:00Z
date_updated: 2025-04-15T07:50:16Z
day: '24'
ddc:
- '510'
- '530'
department:
- _id: MaMo
doi: 10.1088/1742-5468/ac9828
external_id:
  isi:
  - '000889589900001'
file:
- access_level: open_access
  checksum: 01411ffa76d3e380a0446baeb89b1ef7
  content_type: application/pdf
  creator: dernst
  date_created: 2023-02-02T08:35:52Z
  date_updated: 2023-02-02T08:35:52Z
  file_id: '12481'
  file_name: 2022_JourStatisticalMechanics_Mondelli.pdf
  file_size: 1729997
  relation: main_file
  success: 1
file_date_updated: 2023-02-02T08:35:52Z
has_accepted_license: '1'
intvolume: '      2022'
isi: 1
issue: '11'
keyword:
- Statistics
- Probability and Uncertainty
- Statistics and Probability
- Statistical and Nonlinear Physics
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
project:
- _id: 059876FA-7A3F-11EA-A408-12923DDC885E
  name: Prix Lopez-Loretta 2019 - Marco Mondelli
publication: 'Journal of Statistical Mechanics: Theory and Experiment'
publication_identifier:
  issn:
  - 1742-5468
publication_status: published
publisher: IOP Publishing
quality_controlled: '1'
related_material:
  record:
  - id: '10598'
    relation: earlier_version
    status: public
scopus_import: '1'
status: public
title: Approximate message passing with spectral initialization for generalized linear
  models
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 2022
year: '2022'
...