RT Journal Article
T1 Adaptive quadrature schemes for bayesian inference via active learning
A1 Llorente Fernández, Fernando
A1 Martino, Luca
A1 Elvira, Víctor
A1 Delgado Gómez, David
A1 López Santiago, Javier
AB 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.
PB IEEE
SN 2169-3536
YR 2020
FD 2020-11-16
LK https://hdl.handle.net/10016/38013
UL https://hdl.handle.net/10016/38013
LA eng
DS e-Archivo
RD 19 jul. 2024