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A generalized least-squares estimator is used to estimate the direction of the optimal separating hyperplane. The estimated hyperplane is shown to interpolate on the training data. While the direction vector can be consistently estimated, as could be expected from recent results in linear regression, a naive plug-in estimate fails to consistently estimate the intercept. A simple correction, which requires an independent hold-out sample, renders the procedure minimax optimal in many scenarios. The interpolation property of the latter procedure can be retained, but surprisingly depends on the way the labels are encoded.<\/jats:p>","DOI":"10.1093\/biomet\/asad037","type":"journal-article","created":{"date-parts":[[2023,6,8]],"date-time":"2023-06-08T16:02:53Z","timestamp":1686240173000},"page":"291-308","source":"Crossref","is-referenced-by-count":0,"title":["Interpolating discriminant functions in high-dimensional Gaussian latent mixtures"],"prefix":"10.1093","volume":"111","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7462-9360","authenticated-orcid":false,"given":"Xin","family":"Bing","sequence":"first","affiliation":[{"name":"Department of Statistical Sciences, University of Toronto , 700 University Avenue , Toronto M5S 1A1, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Marten","family":"Wegkamp","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Cornell University , 310 Malott Hall , Ithaca, New York 14853, U.S.A . marten.wegkamp@cornell.edu"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2023,6,8]]},"reference":[{"key":"2024060800492417100_asad037-B1","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1111\/1468-0262.00392","article-title":"Inferential theory for factor models of large dimensions","volume":"71","author":"Bai","year":"2003","journal-title":"Econometrica"},{"key":"2024060800492417100_asad037-B2","doi-asserted-by":"crossref","first-page":"304","DOI":"10.1016\/j.jeconom.2008.08.010","article-title":"Forecasting economic time series using targeted predictors","volume":"146","author":"Bai","year":"2008","journal-title":"J. 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