{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,30]],"date-time":"2026-01-30T19:34:29Z","timestamp":1769801669283,"version":"3.49.0"},"reference-count":23,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T00:00:00Z","timestamp":1769126400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12201454"],"award-info":[{"award-number":["12201454"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004543","name":"China Scholarship Council","doi-asserted-by":"publisher","award":["202408120083"],"award-info":[{"award-number":["202408120083"]}],"id":[{"id":"10.13039\/501100004543","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000038","name":"Natural Science and Engineering Research Council of Canada","doi-asserted-by":"crossref","award":["RGPIN-2024-06202"],"award-info":[{"award-number":["RGPIN-2024-06202"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100000038","name":"Natural Science and Engineering Research Council of Canada","doi-asserted-by":"crossref","award":["RGPIN-2023-05655"],"award-info":[{"award-number":["RGPIN-2023-05655"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>High-dimensional regression with multivariate responses poses significant challenges when data are collected across multiple platforms, each with potentially correlated outcomes. In this paper, we introduce a multi-platform multivariate high-dimensional linear regression (MM-HLR) model for simultaneously modeling within-platform correlation and cross-platform information fusion. Our approach incorporates a mixture of Lasso and group Lasso penalties to promote both individual predictor sparsity and cross-platform group sparsity, thereby enhancing interpretability and estimation stability. We develop an efficient computational algorithm based on iteratively reweighted least squares and block coordinate descent to solve the resulting regularized optimization problem. We establish theoretical guarantees for our estimator, including oracle bounds on prediction error, estimation accuracy, and support recovery under mild conditions. Our simulation studies confirm the method\u2019s strong empirical performance, demonstrating low bias, small variance, and robustness across various dimensions. The analysis of real financial data further validates the performance gains achieved by incorporating multivariate responses and integrating data across multiple platforms.<\/jats:p>","DOI":"10.3390\/e28020135","type":"journal-article","created":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T17:52:38Z","timestamp":1769190758000},"page":"135","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Multi-Platform Multivariate Regression with Group Sparsity for High-Dimensional Data Integration"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1325-1936","authenticated-orcid":false,"given":"Shanshan","family":"Qin","sequence":"first","affiliation":[{"name":"School of Statistics, Tianjin University of Finance and Economics, Tianjin 300222, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guanlin","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8057-5100","authenticated-orcid":false,"given":"Xin","family":"Gao","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8858-1289","authenticated-orcid":false,"given":"Yuehua","family":"Wu","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,1,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1093\/biomet\/asx023","article-title":"Data integration with high dimensionality","volume":"104","author":"Gao","year":"2017","journal-title":"Biometrika"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/1471-2105-11-181","article-title":"Multi-task learning for cross-platform siRNA efficacy prediction: An in-silico study","volume":"11","author":"Liu","year":"2010","journal-title":"BMC Bioinform."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"i97","DOI":"10.1093\/bioinformatics\/btq181","article-title":"Sparse multitask regression for identifying common mechanism of response to therapeutic targets","volume":"26","author":"Zhang","year":"2010","journal-title":"Bioinformatics"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"891","DOI":"10.1007\/s10994-023-06410-0","article-title":"Heterogeneous multi-task feature learning with mixed \u21132,1 regularization","volume":"113","author":"Zhong","year":"2024","journal-title":"Mach. 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