[{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","external_id":{"arxiv":["2211.11368"]},"publication_identifier":{"eissn":["2577-0187"]},"publication_status":"published","title":"Precise asymptotics for spectral methods in mixed generalized linear models","citation":{"ieee":"Y. Zhang, M. Mondelli, and R. Venkataramanan, “Precise asymptotics for spectral methods in mixed generalized linear models,” <i>SIAM Journal on Mathematics of Data Science</i>, vol. 8, no. 2. SIAM, pp. 411–439, 2026.","mla":"Zhang, Yihan, et al. “Precise Asymptotics for Spectral Methods in Mixed Generalized Linear Models.” <i>SIAM Journal on Mathematics of Data Science</i>, vol. 8, no. 2, SIAM, 2026, pp. 411–39, doi:<a href=\"https://doi.org/10.1137/24m1702854\">10.1137/24m1702854</a>.","ama":"Zhang Y, Mondelli M, Venkataramanan R. Precise asymptotics for spectral methods in mixed generalized linear models. <i>SIAM Journal on Mathematics of Data Science</i>. 2026;8(2):411-439. doi:<a href=\"https://doi.org/10.1137/24m1702854\">10.1137/24m1702854</a>","short":"Y. Zhang, M. Mondelli, R. Venkataramanan, SIAM Journal on Mathematics of Data Science 8 (2026) 411–439.","apa":"Zhang, Y., Mondelli, M., &#38; Venkataramanan, R. (2026). Precise asymptotics for spectral methods in mixed generalized linear models. <i>SIAM Journal on Mathematics of Data Science</i>. SIAM. <a href=\"https://doi.org/10.1137/24m1702854\">https://doi.org/10.1137/24m1702854</a>","ista":"Zhang Y, Mondelli M, Venkataramanan R. 2026. Precise asymptotics for spectral methods in mixed generalized linear models. SIAM Journal on Mathematics of Data Science. 8(2), 411–439.","chicago":"Zhang, Yihan, Marco Mondelli, and Ramji Venkataramanan. “Precise Asymptotics for Spectral Methods in Mixed Generalized Linear Models.” <i>SIAM Journal on Mathematics of Data Science</i>. SIAM, 2026. <a href=\"https://doi.org/10.1137/24m1702854\">https://doi.org/10.1137/24m1702854</a>."},"article_processing_charge":"Yes (in subscription journal)","doi":"10.1137/24m1702854","day":"01","_id":"22228","keyword":["spectral estimator","generalized linear models","mixed regression","high-dimensional asymptotics","random matrix theory","approximate message passing (AMP)"],"language":[{"iso":"eng"}],"fulldoi":"https://doi.org/10.1137/24m1702854","oa_version":"Published Version","arxiv":1,"issue":"2","article_type":"original","page":"411-439","mathsc":["62E20","62J05","62J12"],"type":"journal_article","project":[{"name":"Prix Lopez-Loretta 2019 - Marco Mondelli","_id":"059876FA-7A3F-11EA-A408-12923DDC885E"}],"has_accepted_license":"1","date_published":"2026-06-01T00:00:00Z","OA_place":"publisher","supplementarymaterial":"no","license":"https://creativecommons.org/licenses/by/4.0/","month":"06","das_tickbox":"0","date_updated":"2026-08-12T06:23:07Z","file":[{"file_id":"22230","file_size":1210346,"content_type":"application/pdf","relation":"main_file","date_created":"2026-07-01T06:22:15Z","success":1,"file_name":"2026_SIAMJourmathDataScience_Zhang.pdf","checksum":"5cfd350dc64d1476063e959316dbff65","creator":"dernst","date_updated":"2026-07-01T06:22:15Z","access_level":"open_access"}],"date_created":"2026-06-30T13:03:41Z","acknowledgement":"The first and second authors were partially supported by the 2019 Lopez-Loreta prize.","department":[{"_id":"MaMo"}],"intvolume":"         8","scopus_import":"1","PlanS_conform":"1","OA_type":"hybrid","quality_controlled":"1","status":"public","ddc":["000"],"researchdata_availability":"no","year":"2026","volume":8,"publication":"SIAM Journal on Mathematics of Data Science","publisher":"SIAM","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"abstract":[{"lang":"eng","text":"In a mixed generalized linear model, the goal is to learn multiple signals from unlabeled observations: each sample comes from exactly one signal, but it is not known which one. We consider the prototypical problem of estimating two statistically independent signals in a mixed generalized linear model with Gaussian covariates. Spectral methods are a popular class of estimators which output the top two eigenvectors of a suitable data-dependent matrix. However, despite the wide applicability, their design is still obtained via heuristic considerations, and the number of samples 𝑛 needed to guarantee recovery is superlinear in the signal dimension 𝑑. In this paper, we develop exact asymptotics on spectral methods in the challenging proportional regime in which 𝑛,𝑑 grow large and their ratio converges to a finite constant. This allows us optimize the design of the spectral method, and combine it with a simple linear estimator, to minimize the estimation error. Our characterization exploits a mix of tools from random matrices, free probability, and the theory of approximate message passing algorithms. Numerical simulations for mixed linear regression and phase retrieval demonstrate the advantage enabled by our analysis over existing designs of spectral methods."}],"corr_author":"1","oa":1,"file_date_updated":"2026-07-01T06:22:15Z","author":[{"last_name":"Zhang","first_name":"Yihan","full_name":"Zhang, Yihan"},{"last_name":"Mondelli","orcid":"0000-0002-3242-7020","id":"27EB676C-8706-11E9-9510-7717E6697425","first_name":"Marco","full_name":"Mondelli, Marco"},{"full_name":"Venkataramanan, Ramji","first_name":"Ramji","last_name":"Venkataramanan"}]},{"title":"Bayesian linear regression for analyzing general omics data with time-to-event phenotypes","publication_status":"published","publication_identifier":{"issn":["2791-4585"]},"supervisor":[{"last_name":"Robinson","full_name":"Robinson, Matthew Richard","orcid":"0000-0001-8982-8813","first_name":"Matthew Richard","id":"E5D42276-F5DA-11E9-8E24-6303E6697425"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","citation":{"chicago":"Villanueva Marijuan, Ariadna. “Bayesian Linear Regression for Analyzing General Omics Data with Time-to-Event Phenotypes.” Institute of Science and Technology Austria, 2024. <a href=\"https://doi.org/10.15479/at:ista:17368\">https://doi.org/10.15479/at:ista:17368</a>.","ista":"Villanueva Marijuan A. 2024. Bayesian linear regression for analyzing general omics data with time-to-event phenotypes. Institute of Science and Technology Austria.","ama":"Villanueva Marijuan A. Bayesian linear regression for analyzing general omics data with time-to-event phenotypes. 2024. doi:<a href=\"https://doi.org/10.15479/at:ista:17368\">10.15479/at:ista:17368</a>","short":"A. Villanueva Marijuan, Bayesian Linear Regression for Analyzing General Omics Data with Time-to-Event Phenotypes, Institute of Science and Technology Austria, 2024.","ieee":"A. Villanueva Marijuan, “Bayesian linear regression for analyzing general omics data with time-to-event phenotypes,” Institute of Science and Technology Austria, 2024.","mla":"Villanueva Marijuan, Ariadna. <i>Bayesian Linear Regression for Analyzing General Omics Data with Time-to-Event Phenotypes</i>. Institute of Science and Technology Austria, 2024, doi:<a href=\"https://doi.org/10.15479/at:ista:17368\">10.15479/at:ista:17368</a>.","apa":"Villanueva Marijuan, A. (2024). <i>Bayesian linear regression for analyzing general omics data with time-to-event phenotypes</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:17368\">https://doi.org/10.15479/at:ista:17368</a>"},"day":"13","_id":"17368","keyword":["Epigenetics","Multi-omics","Bayesian regression"],"oa_version":"Published Version","fulldoi":"https://doi.org/10.15479/at:ista:17368","language":[{"iso":"eng"}],"doi":"10.15479/at:ista:17368","article_processing_charge":"No","type":"dissertation","has_accepted_license":"1","page":"60","month":"08","OA_place":"publisher","supplementarymaterial":"no","doi_confirm":"1","date_published":"2024-08-13T00:00:00Z","department":[{"_id":"GradSch"},{"_id":"MaRo"}],"degree_awarded":"MS","date_created":"2024-08-02T10:52:40Z","file":[{"file_size":13052436,"file_id":"17433","relation":"main_file","content_type":"application/pdf","embargo":"2025-02-14","checksum":"0c2daa174609f0c00919dccc5701d375","date_created":"2024-08-14T11:51:24Z","file_name":"Masters_thesis_AriadnaVillanueva.pdf","creator":"avillanu","access_level":"open_access","date_updated":"2025-02-14T23:30:03Z"},{"relation":"source_file","content_type":"application/zip","file_size":45642547,"file_id":"17434","access_level":"closed","date_updated":"2025-02-14T23:30:03Z","creator":"avillanu","checksum":"e9ed4465dfa539ac4c3a8d4d0b6271a1","date_created":"2024-08-14T11:51:57Z","file_name":"Masters thesis-AriadnaVillanueva.zip","embargo_to":"open_access"}],"das_tickbox":"0","date_updated":"2026-10-02T11:35:19Z","year":"2024","researchdata_availability":"no","status":"public","ddc":["610"],"file_date_updated":"2025-02-14T23:30:03Z","oa":1,"author":[{"last_name":"Villanueva Marijuan","id":"e0ae4864-133f-11ed-8f02-adaa8dd27540","first_name":"Ariadna","full_name":"Villanueva Marijuan, Ariadna"}],"tmp":{"image":"/images/cc_by_nc_sa.png","legal_code_url":"https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode","short":"CC BY-NC-SA (4.0)","name":"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)"},"corr_author":"1","abstract":[{"lang":"eng","text":"Recent advancements in molecular diagnostic techniques have enabled the collection of\r\nmultiple types of omics data from patients, including genomics, epigenomics, proteomics,\r\nand transcriptomics. However, we lack effective methods for integrating all these different\r\ndata types and combining them with clinical outcomes to study the molecular mechanisms\r\nthat govern pathological phenotypes. We present multi-omics BayesW, a penalized Bayesian\r\nregression method that can handle general omics data for survival analysis of time-to-event\r\nphenotypes. Our method can: (1) accommodate incomplete data by allowing censored\r\nindividuals, (2) use continuous time-to-event data to test associations of markers with a\r\nphenotype and (3) estimate effects jointly while allowing for independent groups of biological\r\nmarkers. Extensive simulations using planted signals on real data demonstrate that our model\r\naccurately retrieves the true parameters of the model while controlling for false discoveries\r\nand maintaining the expected prediction accuracy. We address data correlations by estimating\r\nthe effects jointly, even between omic groups, while also estimating the individual variance\r\nexplained by each group. We apply our model to two datasets. Using 18,000 individuals from\r\nthe Generation Scotland study we model the association of time at onset of Type 2 Diabetes,\r\nStroke, Ischemic Disease, and Osteoarthritis from baseline study entry, with 831,724 CpG\r\nmethylation probes. We find that large proportions of variation in disease onset times can\r\nbe attributed to methylation as measured in whole blood at baseline in individuals without\r\ndisease symptoms. We then apply our model to The Cancer Genome Atlas (TCGA) pan-cancer\r\ndataset, in which we use 5 types of omics: copy number variation, epigenetics, somatic\r\nmutations, miRNA, and gene expression. For cancer survival age-at-onset we find that, when\r\nfitting the 5 groups together, almost all variation attributable to \"omics\" data is explained by\r\nDNA methylation. When considering progression times, both methylation and gene expression\r\nexplain a large part of the variance. We found 2 genes that are significantly associated (95%\r\nposterior inclusion probability) with cancer survival time, conditional on all other genome-wide\r\nomics data variation. Owing to the vast variability of mechanisms characterizing different\r\ncancers, there are likely few specific genes with a strong signal in a pan-cancer setting. Taken\r\ntogether, we showed the applicability of our multi-omics BayesW model to a wide-range of\r\nbiological questions in multi-omics data.\r\n"}],"alternative_title":["ISTA Master's Thesis"],"publisher":"Institute of Science and Technology Austria"},{"department":[{"_id":"ChLa"},{"_id":"GaTk"}],"date_created":"2018-12-12T12:31:39Z","file":[{"file_name":"IST-2018-98-v1+1_BBalls_area2_tile2_20x20.mat","date_created":"2018-12-12T13:02:24Z","checksum":"6808748837b9afbbbabc2a356ca2b88a","creator":"system","date_updated":"2020-07-14T12:47:07Z","access_level":"open_access","file_id":"5590","file_size":1142543971,"content_type":"application/octet-stream","relation":"main_file"},{"checksum":"d6d6cd07743038fe3a12352983fcf9dd","date_created":"2018-12-12T13:02:25Z","file_name":"IST-2018-98-v1+2_ExperimentStructure.pdf","access_level":"open_access","date_updated":"2020-07-14T12:47:07Z","creator":"system","file_size":702336,"file_id":"5591","content_type":"application/pdf","relation":"main_file"},{"date_updated":"2020-07-14T12:47:07Z","access_level":"open_access","creator":"system","file_name":"IST-2018-98-v1+3_GoodLocations_area2_20x20.mat","date_created":"2018-12-12T13:02:26Z","checksum":"0c9cfb4dab35bb3dc25a04395600b1c8","relation":"main_file","content_type":"application/octet-stream","file_id":"5592","file_size":432},{"file_size":986,"file_id":"5593","relation":"main_file","content_type":"text/plain","checksum":"2a83b011012e21e934b4596285b1a183","date_created":"2018-12-12T13:02:26Z","file_name":"IST-2018-98-v1+4_README.txt","access_level":"open_access","date_updated":"2020-07-14T12:47:07Z","creator":"system"}],"date_updated":"2025-04-15T08:18:24Z","license":"https://creativecommons.org/publicdomain/zero/1.0/","month":"03","date_published":"2018-03-29T00:00:00Z","file_date_updated":"2020-07-14T12:47:07Z","oa":1,"datarep_id":"98","author":[{"last_name":"Deny","full_name":"Deny, Stephane","first_name":"Stephane"},{"full_name":"Marre, Olivier","first_name":"Olivier","last_name":"Marre"},{"first_name":"Vicente","full_name":"Botella-Soler, Vicente","last_name":"Botella-Soler"},{"last_name":"Martius","full_name":"Martius, Georg S","first_name":"Georg S","id":"3A276B68-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Tkacik, Gasper","orcid":"0000-0002-6699-1455","id":"3D494DCA-F248-11E8-B48F-1D18A9856A87","first_name":"Gasper","last_name":"Tkacik"}],"abstract":[{"text":"This package contains data for the publication \"Nonlinear decoding of a complex movie from the mammalian retina\" by Deny S. et al, PLOS Comput Biol (2018). \r\n\r\nThe data consists of\r\n(i) 91 spike sorted, isolated rat retinal ganglion cells that pass stability and quality criteria, recorded on the multi-electrode array, in response to the presentation of the complex movie with many randomly moving dark discs. The responses are represented as 648000 x 91 binary matrix, where the first index indicates the timebin of duration 12.5 ms, and the second index the neural identity. The matrix entry is 0/1 if the neuron didn't/did spike in the particular time bin.\r\n(ii) README file and a graphical illustration of the structure of the experiment, specifying how the 648000 timebins are split into epochs where 1, 2, 4, or 10 discs  were displayed, and which stimulus segments are exact repeats or unique ball trajectories.\r\n(iii) a 648000 x 400 matrix of luminance traces for each of the 20 x 20 positions (\"sites\") in the movie frame, with time that is locked to the recorded raster. The luminance traces are produced as described in the manuscript by filtering the raw disc movie with a small gaussian spatial kernel. ","lang":"eng"}],"tmp":{"short":"CC0 (1.0)","image":"/images/cc_0.png","legal_code_url":"https://creativecommons.org/publicdomain/zero/1.0/legalcode","name":"Creative Commons Public Domain Dedication (CC0 1.0)"},"publisher":"Institute of Science and Technology Austria","year":"2018","status":"public","ddc":["570"],"citation":{"apa":"Deny, S., Marre, O., Botella-Soler, V., Martius, G. S., &#38; Tkačik, G. (2018). Nonlinear decoding of a complex movie from the mammalian retina. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/AT:ISTA:98\">https://doi.org/10.15479/AT:ISTA:98</a>","short":"S. Deny, O. Marre, V. Botella-Soler, G.S. Martius, G. Tkačik, (2018).","ama":"Deny S, Marre O, Botella-Soler V, Martius GS, Tkačik G. Nonlinear decoding of a complex movie from the mammalian retina. 2018. doi:<a href=\"https://doi.org/10.15479/AT:ISTA:98\">10.15479/AT:ISTA:98</a>","ieee":"S. Deny, O. Marre, V. Botella-Soler, G. S. Martius, and G. Tkačik, “Nonlinear decoding of a complex movie from the mammalian retina.” Institute of Science and Technology Austria, 2018.","mla":"Deny, Stephane, et al. <i>Nonlinear Decoding of a Complex Movie from the Mammalian Retina</i>. Institute of Science and Technology Austria, 2018, doi:<a href=\"https://doi.org/10.15479/AT:ISTA:98\">10.15479/AT:ISTA:98</a>.","chicago":"Deny, Stephane, Olivier Marre, Vicente Botella-Soler, Georg S Martius, and Gašper Tkačik. “Nonlinear Decoding of a Complex Movie from the Mammalian Retina.” Institute of Science and Technology Austria, 2018. <a href=\"https://doi.org/10.15479/AT:ISTA:98\">https://doi.org/10.15479/AT:ISTA:98</a>.","ista":"Deny S, Marre O, Botella-Soler V, Martius GS, Tkačik G. 2018. Nonlinear decoding of a complex movie from the mammalian retina, Institute of Science and Technology Austria, <a href=\"https://doi.org/10.15479/AT:ISTA:98\">10.15479/AT:ISTA:98</a>."},"title":"Nonlinear decoding of a complex movie from the mammalian retina","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","type":"research_data","project":[{"name":"Sensitivity to higher-order statistics in natural scenes","grant_number":"P 25651-N26","call_identifier":"FWF","_id":"254D1A94-B435-11E9-9278-68D0E5697425"}],"has_accepted_license":"1","related_material":{"record":[{"id":"292","status":"public","relation":"used_in_publication"}]},"_id":"5584","day":"29","keyword":["retina","decoding","regression","neural networks","complex stimulus"],"fulldoi":"https://doi.org/10.15479/AT:ISTA:98","oa_version":"Published Version","doi":"10.15479/AT:ISTA:98","article_processing_charge":"No"}]