{"department":[{"_id":"MaMo"}],"publisher":"ML Research Press","day":"01","article_processing_charge":"Yes (via OA deal)","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"publication":"Proceedings of The 24th International Conference on Artificial Intelligence and Statistics","publication_status":"published","_id":"10598","scopus_import":"1","oa":1,"volume":130,"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. "}],"date_created":"2022-01-03T11:34:22Z","editor":[{"full_name":"Banerjee, Arindam","first_name":"Arindam","last_name":"Banerjee"},{"last_name":"Fukumizu","first_name":"Kenji","full_name":"Fukumizu, Kenji"}],"publication_identifier":{"issn":["2640-3498"]},"year":"2021","month":"04","date_published":"2021-04-01T00:00:00Z","citation":{"ieee":"M. Mondelli and R. Venkataramanan, “Approximate message passing with spectral initialization for generalized linear models,” in <i>Proceedings of The 24th International Conference on Artificial Intelligence and Statistics</i>, Virtual, San Diego, CA, United States, 2021, vol. 130, pp. 397–405.","ama":"Mondelli M, Venkataramanan R. Approximate message passing with spectral initialization for generalized linear models. In: Banerjee A, Fukumizu K, eds. <i>Proceedings of The 24th International Conference on Artificial Intelligence and Statistics</i>. Vol 130. ML Research Press; 2021:397-405.","mla":"Mondelli, Marco, and Ramji Venkataramanan. “Approximate Message Passing with Spectral Initialization for Generalized Linear Models.” <i>Proceedings of The 24th International Conference on Artificial Intelligence and Statistics</i>, edited by Arindam Banerjee and Kenji Fukumizu, vol. 130, ML Research Press, 2021, pp. 397–405.","short":"M. Mondelli, R. Venkataramanan, in:, A. Banerjee, K. Fukumizu (Eds.), Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, ML Research Press, 2021, pp. 397–405.","ista":"Mondelli M, Venkataramanan R. 2021. Approximate message passing with spectral initialization for generalized linear models. Proceedings of The 24th International Conference on Artificial Intelligence and Statistics. AISTATS: Artificial Intelligence and Statistics, Proceedings of Machine Learning Research, vol. 130, 397–405.","apa":"Mondelli, M., &#38; Venkataramanan, R. (2021). Approximate message passing with spectral initialization for generalized linear models. In A. Banerjee &#38; K. Fukumizu (Eds.), <i>Proceedings of The 24th International Conference on Artificial Intelligence and Statistics</i> (Vol. 130, pp. 397–405). Virtual, San Diego, CA, United States: ML Research Press.","chicago":"Mondelli, Marco, and Ramji Venkataramanan. “Approximate Message Passing with Spectral Initialization for Generalized Linear Models.” In <i>Proceedings of The 24th International Conference on Artificial Intelligence and Statistics</i>, edited by Arindam Banerjee and Kenji Fukumizu, 130:397–405. ML Research Press, 2021."},"intvolume":"       130","project":[{"_id":"059876FA-7A3F-11EA-A408-12923DDC885E","name":"Prix Lopez-Loretta 2019 - Marco Mondelli"}],"main_file_link":[{"open_access":"1","url":"https://proceedings.mlr.press/v130/mondelli21a.html"}],"quality_controlled":"1","related_material":{"record":[{"id":"12480","relation":"later_version","status":"public"}]},"title":"Approximate message passing with spectral initialization for generalized linear models","acknowledgement":"The authors would like to thank Andrea Montanari for helpful discussions. M. Mondelli was partially supported by the 2019 Lopez-Loreta Prize. R. Venkataramanan was partially supported by the Alan Turing Institute under the EPSRC grant EP/N510129/1.","type":"conference","page":"397-405","date_updated":"2024-03-07T10:36:53Z","alternative_title":["Proceedings of Machine Learning Research"],"oa_version":"Preprint","conference":{"start_date":"2021-04-13","location":"Virtual, San Diego, CA, United States","name":"AISTATS: Artificial Intelligence and Statistics","end_date":"2021-04-15"},"author":[{"last_name":"Mondelli","first_name":"Marco","orcid":"0000-0002-3242-7020","id":"27EB676C-8706-11E9-9510-7717E6697425","full_name":"Mondelli, Marco"},{"first_name":"Ramji","last_name":"Venkataramanan","full_name":"Venkataramanan, Ramji"}],"status":"public","external_id":{"arxiv":["2010.03460"]}}