[{"file_date_updated":"2023-02-02T08:35:52Z","quality_controlled":"1","article_type":"original","publisher":"IOP Publishing","author":[{"first_name":"Marco","last_name":"Mondelli","orcid":"0000-0002-3242-7020","full_name":"Mondelli, Marco","id":"27EB676C-8706-11E9-9510-7717E6697425"},{"first_name":"Ramji","last_name":"Venkataramanan","full_name":"Venkataramanan, Ramji"}],"issue":"11","_id":"12480","scopus_import":"1","title":"Approximate message passing with spectral initialization for generalized linear models","intvolume":"      2022","publication_status":"published","department":[{"_id":"MaMo"}],"article_processing_charge":"Yes (via OA deal)","date_created":"2023-02-02T08:31:57Z","ddc":["510","530"],"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.","volume":2022,"isi":1,"external_id":{"isi":["000889589900001"]},"date_updated":"2024-03-07T10:36:52Z","citation":{"short":"M. Mondelli, R. Venkataramanan, Journal of Statistical Mechanics: Theory and Experiment 2022 (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>.","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.","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>","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>","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."},"year":"2022","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."}],"doi":"10.1088/1742-5468/ac9828","day":"24","language":[{"iso":"eng"}],"keyword":["Statistics","Probability and Uncertainty","Statistics and Probability","Statistical and Nonlinear Physics"],"publication":"Journal of Statistical Mechanics: Theory and Experiment","has_accepted_license":"1","month":"11","article_number":"114003","oa_version":"Published Version","project":[{"name":"Prix Lopez-Loretta 2019 - Marco Mondelli","_id":"059876FA-7A3F-11EA-A408-12923DDC885E"}],"related_material":{"record":[{"status":"public","relation":"earlier_version","id":"10598"}]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","file":[{"relation":"main_file","success":1,"access_level":"open_access","file_id":"12481","creator":"dernst","date_created":"2023-02-02T08:35:52Z","file_size":1729997,"checksum":"01411ffa76d3e380a0446baeb89b1ef7","date_updated":"2023-02-02T08:35:52Z","content_type":"application/pdf","file_name":"2022_JourStatisticalMechanics_Mondelli.pdf"}],"date_published":"2022-11-24T00:00:00Z","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"oa":1,"publication_identifier":{"issn":["1742-5468"]}},{"abstract":[{"text":"While several tools have been developed to study the ground state of many-body quantum spin systems, the limitations of existing techniques call for the exploration of new approaches. In this manuscript we develop an alternative analytical and numerical framework for many-body quantum spin ground states, based on the disentanglement formalism. In this approach, observables are exactly expressed as Gaussian-weighted functional integrals over scalar fields. We identify the leading contribution to these integrals, given by the saddle point of a suitable effective action. Analytically, we develop a field-theoretical expansion of the functional integrals, performed by means of appropriate Feynman rules. The expansion can be truncated to a desired order to obtain analytical approximations to observables. Numerically, we show that the disentanglement approach can be used to compute ground state expectation values from classical stochastic processes. While the associated fluctuations grow exponentially with imaginary time and the system size, this growth can be mitigated by means of an importance sampling scheme based on knowledge of the saddle point configuration. We illustrate the advantages and limitations of our methods by considering the quantum Ising model in 1, 2 and 3 spatial dimensions. Our analytical and numerical approaches are applicable to a broad class of systems, bridging concepts from quantum lattice models, continuum field theory, and classical stochastic processes.","lang":"eng"}],"day":"05","doi":"10.1088/1742-5468/abc7c7","external_id":{"isi":["000605080300001"]},"isi":1,"citation":{"chicago":"De Nicola, Stefano. “Disentanglement Approach to Quantum Spin Ground States: Field Theory and Stochastic Simulation.” <i>Journal of Statistical Mechanics: Theory and Experiment</i>. IOP Publishing, 2021. <a href=\"https://doi.org/10.1088/1742-5468/abc7c7\">https://doi.org/10.1088/1742-5468/abc7c7</a>.","ieee":"S. De Nicola, “Disentanglement approach to quantum spin ground states: Field theory and stochastic simulation,” <i>Journal of Statistical Mechanics: Theory and Experiment</i>, vol. 2021, no. 1. IOP Publishing, 2021.","ama":"De Nicola S. Disentanglement approach to quantum spin ground states: Field theory and stochastic simulation. <i>Journal of Statistical Mechanics: Theory and Experiment</i>. 2021;2021(1). doi:<a href=\"https://doi.org/10.1088/1742-5468/abc7c7\">10.1088/1742-5468/abc7c7</a>","apa":"De Nicola, S. (2021). Disentanglement approach to quantum spin ground states: Field theory and stochastic simulation. <i>Journal of Statistical Mechanics: Theory and Experiment</i>. IOP Publishing. <a href=\"https://doi.org/10.1088/1742-5468/abc7c7\">https://doi.org/10.1088/1742-5468/abc7c7</a>","ista":"De Nicola S. 2021. Disentanglement approach to quantum spin ground states: Field theory and stochastic simulation. Journal of Statistical Mechanics: Theory and Experiment. 2021(1), 013101.","short":"S. De Nicola, Journal of Statistical Mechanics: Theory and Experiment 2021 (2021).","mla":"De Nicola, Stefano. “Disentanglement Approach to Quantum Spin Ground States: Field Theory and Stochastic Simulation.” <i>Journal of Statistical Mechanics: Theory and Experiment</i>, vol. 2021, no. 1, 013101, IOP Publishing, 2021, doi:<a href=\"https://doi.org/10.1088/1742-5468/abc7c7\">10.1088/1742-5468/abc7c7</a>."},"year":"2021","date_updated":"2023-08-07T13:46:28Z","ddc":["530"],"acknowledgement":"S D N would like to thank M J Bhaseen, J Chalker, B Doyon, V Gritsev, A Lamacraft,\r\nA Michailidis and M Serbyn for helpful feedback and stimulating conversations. S D N\r\nacknowledges funding from the Institute of Science and Technology (IST) Austria, and\r\nfrom the European Union’s Horizon 2020 research and innovation program under the\r\nMarie Sk\blodowska-Curie Grant Agreement No. 754411. S D N also acknowledges funding\r\nfrom the EPSRC Center for Doctoral Training in Cross-Disciplinary Approaches to Non-\r\nEquilibrium Systems (CANES) under Grant EP/L015854/1. S D N is grateful to IST\r\nAustria for providing open access funding.","volume":2021,"intvolume":"      2021","title":"Disentanglement approach to quantum spin ground states: Field theory and stochastic simulation","department":[{"_id":"MaSe"}],"date_created":"2021-02-17T17:48:46Z","article_processing_charge":"No","publication_status":"published","issue":"1","author":[{"first_name":"Stefano","last_name":"De Nicola","orcid":"0000-0002-4842-6671","full_name":"De Nicola, Stefano","id":"42832B76-F248-11E8-B48F-1D18A9856A87"}],"_id":"9158","article_type":"original","publisher":"IOP Publishing","file_date_updated":"2021-02-19T14:04:40Z","ec_funded":1,"quality_controlled":"1","oa":1,"publication_identifier":{"issn":["1742-5468"]},"type":"journal_article","date_published":"2021-01-05T00:00:00Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","file":[{"file_name":"2021_JourStatMech_deNicola.pdf","content_type":"application/pdf","date_updated":"2021-02-19T14:04:40Z","file_size":1693609,"checksum":"64e2aae4837790db26e1dd1986c69c07","date_created":"2021-02-19T14:04:40Z","creator":"dernst","file_id":"9172","relation":"main_file","access_level":"open_access","success":1}],"article_number":"013101","month":"01","project":[{"name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"oa_version":"Published Version","has_accepted_license":"1","publication":"Journal of Statistical Mechanics: Theory and Experiment","keyword":["Statistics","Probability and Uncertainty","Statistics and Probability","Statistical and Nonlinear Physics"],"language":[{"iso":"eng"}]},{"volume":2019,"acknowledgement":"We acknowledge interesting discussions with M Abbott, E Aurell, J Barbier, R Monasson, T Mora, I Nemenman, N Tishby and R Zecchina. This research was supported by the Kavli Foundation and the Centre of Excellence scheme of the Research Council of Norway (Centre for Neural Computation) (RJC and YR), by the Basic Science Research Program through the National Research Foundation of Korea (NRF), funded by the Ministry of Education (2016R1D1A1B03932264) (JJ), and, in part, by the ICTP through the OEA-AC-98 (JS).","extern":"1","doi":"10.1088/1742-5468/ab16c8","arxiv":1,"day":"17","abstract":[{"text":"We show that statistical criticality, i.e. the occurrence of power law frequency distributions, arises in samples that are maximally informative about the underlying generating process. In order to reach this conclusion, we first identify the frequency with which different outcomes occur in a sample, as the variable carrying useful information on the generative process. The entropy of the frequency, that we call relevance, provides an upper bound to the number of informative bits. This differs from the entropy of the data, that we take as a measure of resolution. Samples that maximise relevance at a given resolution—that we call maximally informative samples—exhibit statistical criticality. In particular, Zipf's law arises at the optimal trade-off between resolution (i.e. compression) and relevance. As a byproduct, we derive a bound of the maximal number of parameters that can be estimated from a dataset, in the absence of prior knowledge on the generative model.\r\n\r\nFurthermore, we relate criticality to the statistical properties of the representation of the data generating process. We show that, as a consequence of the concentration property of the asymptotic equipartition property, representations that are maximally informative about the data generating process are characterised by an exponential distribution of energy levels. This arises from a principle of minimal entropy, that is conjugate of the maximum entropy principle in statistical mechanics. This explains why statistical criticality requires no parameter fine tuning in maximally informative samples.","lang":"eng"}],"date_updated":"2021-01-12T08:11:57Z","year":"2019","citation":{"ieee":"R. J. Cubero, J. Jo, M. Marsili, Y. Roudi, and J. Song, “Statistical criticality arises in most informative representations,” <i>Journal of Statistical Mechanics: Theory and Experiment</i>, vol. 2019, no. 6. IOP Publishing, 2019.","chicago":"Cubero, Ryan J, Junghyo Jo, Matteo Marsili, Yasser Roudi, and Juyong Song. “Statistical Criticality Arises in Most Informative Representations.” <i>Journal of Statistical Mechanics: Theory and Experiment</i>. IOP Publishing, 2019. <a href=\"https://doi.org/10.1088/1742-5468/ab16c8\">https://doi.org/10.1088/1742-5468/ab16c8</a>.","ama":"Cubero RJ, Jo J, Marsili M, Roudi Y, Song J. Statistical criticality arises in most informative representations. <i>Journal of Statistical Mechanics: Theory and Experiment</i>. 2019;2019(6). doi:<a href=\"https://doi.org/10.1088/1742-5468/ab16c8\">10.1088/1742-5468/ab16c8</a>","apa":"Cubero, R. J., Jo, J., Marsili, M., Roudi, Y., &#38; Song, J. (2019). Statistical criticality arises in most informative representations. <i>Journal of Statistical Mechanics: Theory and Experiment</i>. IOP Publishing. <a href=\"https://doi.org/10.1088/1742-5468/ab16c8\">https://doi.org/10.1088/1742-5468/ab16c8</a>","ista":"Cubero RJ, Jo J, Marsili M, Roudi Y, Song J. 2019. Statistical criticality arises in most informative representations. Journal of Statistical Mechanics: Theory and Experiment. 2019(6), 063402.","mla":"Cubero, Ryan J., et al. “Statistical Criticality Arises in Most Informative Representations.” <i>Journal of Statistical Mechanics: Theory and Experiment</i>, vol. 2019, no. 6, 063402, IOP Publishing, 2019, doi:<a href=\"https://doi.org/10.1088/1742-5468/ab16c8\">10.1088/1742-5468/ab16c8</a>.","short":"R.J. Cubero, J. Jo, M. Marsili, Y. Roudi, J. Song, Journal of Statistical Mechanics: Theory and Experiment 2019 (2019)."},"external_id":{"arxiv":["1808.00249"]},"publisher":"IOP Publishing","article_type":"original","quality_controlled":"1","publication_status":"published","date_created":"2019-11-26T22:36:09Z","article_processing_charge":"No","title":"Statistical criticality arises in most informative representations","intvolume":"      2019","_id":"7130","author":[{"id":"850B2E12-9CD4-11E9-837F-E719E6697425","last_name":"Cubero","first_name":"Ryan J","full_name":"Cubero, Ryan J","orcid":"0000-0003-0002-1867"},{"last_name":"Jo","first_name":"Junghyo","full_name":"Jo, Junghyo"},{"last_name":"Marsili","first_name":"Matteo","full_name":"Marsili, Matteo"},{"full_name":"Roudi, Yasser","first_name":"Yasser","last_name":"Roudi"},{"full_name":"Song, Juyong","last_name":"Song","first_name":"Juyong"}],"issue":"6","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1808.00249"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","publication_identifier":{"issn":["1742-5468"]},"oa":1,"date_published":"2019-06-17T00:00:00Z","type":"journal_article","language":[{"iso":"eng"}],"keyword":["optimization under uncertainty","source coding","large deviation"],"oa_version":"Preprint","month":"06","article_number":"063402","publication":"Journal of Statistical Mechanics: Theory and Experiment"}]