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It does so by leveraging block-matrix identities to incrementally reuse inverses and determinants from smaller GP kernel matrices to accelerate computations on larger ones without sacrificing numerical precision. By casting successive trial-length extensions as Schur-complement updates, our method reduces the cost of each new inversion to depend only on the size difference between matrices. We demonstrate that this approach yields more than twofold speed-ups over direct and persymmetric inversion baselines on both synthetic data sets and data from neural recordings. In an additional comparison to sparse inducing-point GPFA, sparse inference reduced inference time for small inducing sets at the expense of worse model fits, while optimizing inducing locations was slower than our exact GPFA variant when the optimization cost was included. We also provide a scikit-learn\u2013compatible Python GPFA package, BlockInverseGPFA, and introduce a variance\u2013explained metric for model evaluation.<\/jats:p>","DOI":"10.1162\/neco.a.1592","type":"journal-article","created":{"date-parts":[[2026,10,9]],"date-time":"2026-10-09T18:35:43Z","timestamp":1791570943000},"page":"2141-2168","update-policy":"https:\/\/doi.org\/10.1162\/mitpressjournals.corrections.policy","source":"Crossref","is-referenced-by-count":0,"title":["Efficient Exact Gaussian Process Inference via Incremental Block-Matrix Identity Updates"],"prefix":"10.1162","volume":"38","author":[{"given":"Brooks M.","family":"Musangu","sequence":"first","affiliation":[{"name":"Department of Neurobiology, Harvard Medical School, Boston, MA 02115, U.S.A. brooks_musangu@hms.harvard.edu"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jan","family":"Drugowitsch","sequence":"additional","affiliation":[{"name":"Department of Neurobiology, Harvard Medical School, 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