Zobrazeno 1 - 10
of 20
pro vyhledávání: '"Daniel Sanz-Alonso"'
Autor:
Daniel Sanz-Alonso, Zijian Wang
Publikováno v:
Entropy, Vol 23, Iss 1, p 22 (2020)
Importance sampling is used to approximate Bayes’ rule in many computational approaches to Bayesian inverse problems, data assimilation and machine learning. This paper reviews and further investigates the required sample size for importance sampli
Externí odkaz:
https://doaj.org/article/90cea68ac4ac4c9fa732d1861716e85a
Publikováno v:
Entropy, Vol 21, Iss 5, p 511 (2019)
The aim of this paper is to provide new theoretical and computational understanding on two loss regularizations employed in deep learning, known as local entropy and heat regularization. For both regularized losses, we introduce variational character
Externí odkaz:
https://doaj.org/article/ea84a397a6694939844903abfebd1a8c
Publikováno v:
SIAM Journal on Mathematics of Data Science. 4:801-833
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::bf4132feafb9be21661798c59f3f66a6
https://doi.org/10.1137/21m1434477
https://doi.org/10.1137/21m1434477
Autor:
Daniel Sanz-Alonso, Ruiyi Yang
Publikováno v:
Statistical Science. 37
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::d2ed3e8e8e35c838ac1afeab5325e4df
https://doi.org/10.1214/21-sts838
https://doi.org/10.1214/21-sts838
Autor:
Daniel Sanz-Alonso, Ruiyi Yang
The stochastic partial differential equation approach to Gaussian processes (GPs) represents Mat\'ern GP priors in terms of $n$ finite element basis functions and Gaussian coefficients with sparse precision matrix. Such representations enhance the sc
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::83924761474c9a22969d839b30d7ec06
http://arxiv.org/abs/2109.02777
http://arxiv.org/abs/2109.02777
Publikováno v:
Bayesian Anal. 15, no. 1 (2020), 29-56
The Bayesian update can be viewed as a variational problem by characterizing the posterior as the minimizer of a functional. The variational viewpoint is far from new and is at the heart of popular methods for posterior approximation. However, some o
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ce65f0c33f73af05792aea664f7915da
https://doi.org/10.1214/18-ba1137
https://doi.org/10.1214/18-ba1137
Publikováno v:
arXiv
This paper suggests a framework for the learning of discretizations of expensive forward models in Bayesian inverse problems. The main idea is to incorporate the parameters governing the discretization as part of the unknown to be estimated within th
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a02a92b4f76f7ad495b01e26ea1782c0
https://hdl.handle.net/1721.1/134038
https://hdl.handle.net/1721.1/134038
Publikováno v:
Inverse Problems. 38:035006
This paper develops manifold learning techniques for the numerical solution of PDE-constrained Bayesian inverse problems on manifolds with boundaries. We introduce graphical Matérn-type Gaussian field priors that enable flexible modeling near the bo
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8f0b93e4ce17798109261c0a3a112ef6
https://doi.org/10.1088/1361-6420/ac3994
https://doi.org/10.1088/1361-6420/ac3994
Publikováno v:
SIAM Journal on Mathematical Analysis. 50:4020-4040
We consider the problem of recovering a function input of a differential equation formulated on an unknown domain $\mathcal{M}$. We assume to have access to a discrete domain $\mathcal{M}_n=\{\math...
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::157272acd7cef829e7a55976febafd24
https://doi.org/10.1137/17m1138005
https://doi.org/10.1137/17m1138005
Autor:
Daniel Sanz-Alonso
Publikováno v:
SIAM/ASA Journal on Uncertainty Quantification. 6:867-879
Importance sampling approximates expectations with respect to a target measure by using samples from a proposal measure. The performance of the method over large classes of test functions depends heavily on the closeness between both measures. We der
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bda1e2d44d15cd8bb945461d258bee62
https://doi.org/10.1137/16m1093549
https://doi.org/10.1137/16m1093549