{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,6]],"date-time":"2026-01-06T13:35:57Z","timestamp":1767706557222,"version":"3.37.3"},"reference-count":0,"publisher":"IOS Press","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2016]]},"abstract":"<jats:p>Gaussian Process Regression (GPR) is a powerful non-parametric method. However, GPR may perform poorly if the data are contaminated by outliers. To address the issue, we replace the Gaussian process with a Student-t process and introduce dependent Student-t noise in this paper, leading to a Student-t Process Regression with Dependent Student-t noise model (TPRD). Closed form expressions for the marginal likelihood and predictive distribution of TPRD are derived. Besides, TPRD gives a probabilistic interpretation to the Student-t Process Regression with the noise incorporated into its Kernel (TPRK), which is a common approach for the Student-t process regression. Moreover, we analyze the influence of different kernels. If the kernel meets a condition, called &amp;beta;-property here, the maximum marginal likelihood estimation of TPRD's hyperparameters is independent of the degrees of freedom &amp;nu; of the Student-t process, which implies that GPR, TPRD and TPRK have exactly the same predictive mean. Empirically, the degrees of freedom &amp;nu; could be regarded as a convergence accelerator, indicating that TPRD with a suitable &amp;nu; performs faster than GPR. If the kernel does not have the &amp;beta;-property, TPRD has better performances than GPR, without additional computational cost. On benchmark datasets, the proposed results are verified.<\/jats:p>","DOI":"10.3233\/978-1-61499-672-9-82","type":"book-chapter","created":{"date-parts":[[2025,2,24]],"date-time":"2025-02-24T11:58:24Z","timestamp":1740398304000},"source":"Crossref","is-referenced-by-count":1,"title":["Student-t Process Regression with Dependent Student-t Noise"],"prefix":"10.3233","author":[{"family":"Tang Qingtao","sequence":"additional","affiliation":[]},{"family":"Wang Yisen","sequence":"additional","affiliation":[]},{"family":"Xia Shu-Tao","sequence":"additional","affiliation":[]}],"member":"7437","container-title":["Frontiers in Artificial Intelligence and Applications","ECAI 2016"],"original-title":[],"deposited":{"date-parts":[[2025,2,24]],"date-time":"2025-02-24T12:08:10Z","timestamp":1740398890000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.medra.org\/servlet\/aliasResolver?alias=iospressISBN&isbn=978-1-61499-671-2&spage=82&doi=10.3233\/978-1-61499-672-9-82"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016]]},"references-count":0,"URL":"https:\/\/doi.org\/10.3233\/978-1-61499-672-9-82","relation":{},"ISSN":["0922-6389"],"issn-type":[{"value":"0922-6389","type":"print"}],"subject":[],"published":{"date-parts":[[2016]]}}}