Interpolation in reproducing kernel Hilbert spaces based on random subdivision schemes

详细信息    查看全文

• 作者：Mariantonia Cotronei^a ; ^{mariantonia.cotronei@unirc.it" class="auth_mail" title="E-mail the corresponding author} ; Rosa Di Salvo^b ; ^{rdisalvo@unime.it" class="auth_mail" title="E-mail the corresponding author} ; Matthias Holschneider^c ; ^{hols@uni-potsdam.de" class="auth_mail" title="E-mail the corresponding author} ; Luigia Puccio^b ; ^{gina@unime.it" class="auth_mail" title="E-mail the corresponding author}
• 关键词：65D05 ; 62F15 ; 41A05 ; 65D10 ; 60G15
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：311
• 期：Complete
• 页码：342-353
• 全文大小：1108 K

文摘

In this paper we present a Bayesian framework for interpolating data in a reproducing kernel Hilbert space associated with a random subdivision scheme, where not only approximations of the values of a function at some missing points can be obtained, but also uncertainty estimates for such predicted values. This random scheme generalizes the usual subdivision by taking into account, at each level, some uncertainty given in terms of suitably scaled noise sequences of i.i.d. Gaussian random variables with zero mean and given variance, and generating, in the limit, a Gaussian process whose correlation structure is characterized and used for computing realizations of the conditional posterior distribution. The hierarchical nature of the procedure may be exploited to reduce the computational cost compared to standard techniques in the case where many prediction points need to be considered.