{"issue":"11","publication_status":"published","date_published":"2022-11-24T00:00:00Z","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."}],"department":[{"_id":"MaMo"}],"day":"24","file":[{"date_updated":"2023-02-02T08:35:52Z","file_id":"12481","success":1,"file_size":1729997,"date_created":"2023-02-02T08:35:52Z","relation":"main_file","checksum":"01411ffa76d3e380a0446baeb89b1ef7","content_type":"application/pdf","file_name":"2022_JourStatisticalMechanics_Mondelli.pdf","creator":"dernst","access_level":"open_access"}],"type":"journal_article","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"date_updated":"2024-03-07T10:36:52Z","article_processing_charge":"Yes (via OA deal)","month":"11","related_material":{"record":[{"id":"10598","relation":"earlier_version","status":"public"}]},"status":"public","quality_controlled":"1","title":"Approximate message passing with spectral initialization for generalized linear models","date_created":"2023-02-02T08:31:57Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa":1,"oa_version":"Published Version","scopus_import":"1","publisher":"IOP Publishing","article_type":"original","citation":{"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.","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).","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>","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.","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>."},"language":[{"iso":"eng"}],"article_number":"114003","_id":"12480","doi":"10.1088/1742-5468/ac9828","author":[{"first_name":"Marco","last_name":"Mondelli","id":"27EB676C-8706-11E9-9510-7717E6697425","full_name":"Mondelli, Marco","orcid":"0000-0002-3242-7020"},{"full_name":"Venkataramanan, Ramji","first_name":"Ramji","last_name":"Venkataramanan"}],"has_accepted_license":"1","publication":"Journal of Statistical Mechanics: Theory and Experiment","publication_identifier":{"issn":["1742-5468"]},"external_id":{"isi":["000889589900001"]},"keyword":["Statistics","Probability and Uncertainty","Statistics and Probability","Statistical and Nonlinear Physics"],"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.","file_date_updated":"2023-02-02T08:35:52Z","isi":1,"ddc":["510","530"],"project":[{"_id":"059876FA-7A3F-11EA-A408-12923DDC885E","name":"Prix Lopez-Loretta 2019 - Marco Mondelli"}],"volume":2022,"intvolume":"      2022","year":"2022"}