✦ LIBER ✦

Derivative reproducing properties for kernel methods in learning theory

✍ Scribed by Ding-Xuan Zhou

Publisher: Elsevier Science
Year: 2008
Tongue: English
Weight: 175 KB
Volume: 220
Category: Article
ISSN: 0377-0427
DOI: 10.1016/j.cam.2007.08.023

No coin nor oath required. For personal study only.

✦ Synopsis

The regularity of functions from reproducing kernel Hilbert spaces (RKHSs) is studied in the setting of learning theory. We provide a reproducing property for partial derivatives up to order s when the Mercer kernel is C 2s . For such a kernel on a general domain we show that the RKHS can be embedded into the function space C s . These observations yield a representer theorem for regularized learning algorithms involving data for function values and gradients. Examples of Hermite learning and semi-supervised learning penalized by gradients on data are considered.

📜 SIMILAR VOLUMES

Method of local-scaling transformations

Method of local-scaling transformations and density functional theory in quantum chemistry. II. The procedure for reproducing a many-electron wave function from x-ray diffraction data on one-electron density

✍ Eugene S. Kryachko; Ivan Zh. Petkov; Mario V. Stoitsov 📂 Article 📅 1987 🏛 John Wiley and Sons 🌐 English ⚖ 343 KB

Renal insufficiency and anemia are indep

Renal insufficiency and anemia are independent risk factors for death among patients with acute myocardial infarction1,21As published material, the contents of this manuscript may not be cited, quoted, reproduced or published without the consent of the authors.2The analyses upon which this publication is based were performed under Contract Number 500-96-P704, entitled âOperation Utilization and Quality Control Peer Review Organization (PRO) for the State of Georgiaâ and sponsored by the Centers for Medicare and Medicaid Services (CMS), Department of Health and Human Services. The conclusions and opinions expressed, and methods used herein are those of the authors. They do not necessarily reflect CMS policy. The authors assume full responsibility for the accuracy and completeness of the ideas presented. This article is a direct result of the Health Care Quality Improvement Program initiated by CMS, which has encouraged identification of quality improvement projects derived from analysis of patterns of care, and therefore required no special funding on the part of this Contractor. Ideas and contributions to the authors concerning experience in engaging with issues presented are welcomed.

✍ Langston, Robert D.; Presley, Rodney; Flanders, W. Dana; Mcclellan, William M. 📂 Article 📅 2003 🏛 Nature Publishing Group 🌐 English ⚖ 373 KB