{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,22]],"date-time":"2025-10-22T23:38:20Z","timestamp":1761176300377,"version":"build-2065373602"},"reference-count":0,"publisher":"IOS Press","isbn-type":[{"value":"9781643686318","type":"electronic"}],"license":[{"start":{"date-parts":[[2025,10,21]],"date-time":"2025-10-21T00:00:00Z","timestamp":1761004800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,10,21]]},"abstract":"<jats:p>Probabilistic Partial Least Squares (PPLS) extends Partial Least Squares (PLS) by incorporating a probabilistic framework and identifiability constraints. PPLS models the relationship between two datasets as the sum of a joint component comprising correlated latent vectors and a noise component of isotropic normal random vectors. However, estimating PPLS model parameters involves a challenging nonconvex constrained optimization problem. We propose the Scalar Likelihood Method (SLM) to estimate the parameters of the PPLS model using a scalar likelihood function of the observed variables, derived via a novel rank n update technique. This technique avoids introducing additional constraints that would compromise the model\u2019s dimension reduction properties. In addition, we derive a closed-form solution for the noise distribution in the observed data, significantly reducing parameter coupling in the objective function, thereby greatly improving parameter estimation quality. Through simulation studies, as well as association analysis and prediction tasks, we demonstrate the effectiveness and efficiency of SLM, highlighting its potential in practical applications.<\/jats:p>","DOI":"10.3233\/faia251416","type":"book-chapter","created":{"date-parts":[[2025,10,22]],"date-time":"2025-10-22T10:01:55Z","timestamp":1761127315000},"source":"Crossref","is-referenced-by-count":0,"title":["Scalar Likelihood Method for Probabilistic Partial Least Squares Model with Rank n Update"],"prefix":"10.3233","author":[{"given":"Haoran","family":"Hu","sequence":"first","affiliation":[{"name":"School of Artificial Intelligence, Beijing Normal University, Beijing, 100875, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xingce","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Artificial Intelligence, Beijing Normal University, Beijing, 100875, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhongke","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Artificial Intelligence, Beijing Normal University, Beijing, 100875, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shilei","family":"Du","sequence":"additional","affiliation":[{"name":"School of Artificial Intelligence, Beijing Normal University, Beijing, 100875, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuhe","family":"Zhang","sequence":"additional","affiliation":[{"name":"Northwest University, Xi\u2019an, 710069, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Quansheng","family":"Liu","sequence":"additional","affiliation":[{"name":"Univ Bretagne Sud, CNRS UMR 6205, LMBA, F-56000, Vannes, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"7437","container-title":["Frontiers in Artificial Intelligence and Applications","ECAI 2025"],"original-title":[],"link":[{"URL":"https:\/\/ebooks.iospress.nl\/pdf\/doi\/10.3233\/FAIA251416","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,22]],"date-time":"2025-10-22T10:01:56Z","timestamp":1761127316000},"score":1,"resource":{"primary":{"URL":"https:\/\/ebooks.iospress.nl\/doi\/10.3233\/FAIA251416"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,21]]},"ISBN":["9781643686318"],"references-count":0,"URL":"https:\/\/doi.org\/10.3233\/faia251416","relation":{},"ISSN":["0922-6389","1879-8314"],"issn-type":[{"value":"0922-6389","type":"print"},{"value":"1879-8314","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,10,21]]}}}