Adaptive quadrature schemes for bayesian inference via active learning

Llorente Fernández, Fernando; Martino, Luca; Elvira, Víctor; Delgado Gómez, David; López Santiago, Javier

Publication:
Adaptive quadrature schemes for bayesian inference via active learning

dc.affiliation.dpto	UC3M. Departamento de Teoría de la Señal y Comunicaciones	es
dc.affiliation.dpto	UC3M. Departamento de Estadística	es
dc.affiliation.grupoinv	UC3M. Grupo de Investigación: Tratamiento de la Señal y Aprendizaje (GTSA)	es
dc.contributor.author	Llorente Fernández, Fernando
dc.contributor.author	Martino, Luca
dc.contributor.author	Elvira, Víctor
dc.contributor.author	Delgado Gómez, David
dc.contributor.author	López Santiago, Javier
dc.date.accessioned	2023-07-28T10:55:44Z
dc.date.available	2023-07-28T10:55:44Z
dc.date.issued	2020-11-16
dc.description.abstract	We propose novel adaptive quadrature schemes based on an active learning procedure. We consider an interpolative approach for building a surrogate posterior density, combining it with Monte Carlo sampling methods and other quadrature rules. The nodes of the quadrature are sequentially chosen by maximizing a suitable acquisition function, which takes into account the current approximation of the posterior and the positions of the nodes. This maximization does not require additional evaluations of the true posterior. We introduce two specific schemes based on Gaussian and Nearest Neighbors bases. For the Gaussian case, we also provide a novel procedure for fitting the bandwidth parameter, in order to build a suitable emulator of a density function. With both techniques, we always obtain a positive estimation of the marginal likelihood (a.k.a., Bayesian evidence). An equivalent importance sampling interpretation is also described, which allows the design of extended schemes. Several theoretical results are provided and discussed. Numerical results show the advantage of the proposed approach, including a challenging inference problem in an astronomic dynamical model, with the goal of revealing the number of planets orbiting a star.	en
dc.format.extent	22
dc.identifier.bibliographicCitation	Fernández, F., Martino, L., Elvira, V., Delgado, D., & López-Santiago, J. (2020). Adaptive quadrature schemes for Bayesian inference via active learning. IEEE Access, 8, 208462-208483.	en
dc.identifier.doi	https://doi.org/10.1109/ACCESS.2020.3038333
dc.identifier.issn	2169-3536
dc.identifier.publicationfirstpage	208462
dc.identifier.publicationlastpage	208483
dc.identifier.publicationtitle	IEEE Access	en
dc.identifier.publicationvolume	8
dc.identifier.uri	https://hdl.handle.net/10016/38013
dc.identifier.uxxi	AR/0000027354
dc.language.iso	eng	en
dc.publisher	IEEE	en
dc.rights	© 2020, The Author(s).	en
dc.rights	Atribución-NoComercial-SinDerivadas 3.0 España	*
dc.rights.accessRights	open access	en
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/3.0/es/	*
dc.subject.eciencia	Estadística	es
dc.subject.eciencia	Telecomunicaciones	es
dc.subject.other	Active learning	en
dc.subject.other	Bayesian quadrature	en
dc.subject.other	Emulation	en
dc.subject.other	Experimental design	en
dc.subject.other	Monte Carlo methods	en
dc.subject.other	Numerical integration	en
dc.title	Adaptive quadrature schemes for bayesian inference via active learning	en
dc.type	research article	*
dc.type.hasVersion	VoR	*
dspace.entity.type	Publication