Speaker
Elle Buser
(Emory University)
Description
We propose a natural gradient descent (NGD) method for efficient hyperparameter estimation in Bayesian inverse problems. In this framework, the objective is formulated as a function of a symmetric positive definite (SPD) matrix that depends on the hyperparameters. Rather than optimizing purely in the parameter space, we define a natural gradient that incorporates information about the model space (i.e. the space of SPD matrices) into the gradient descent by equipping the manifold with a Riemannian metric. We consider two metrics, the Log-Cholesky and Log-Euclidean metric, both designed for SPD matrices. Finally, we present a numerical example comparing the performance of NGD based on different metrics to the standard gradient descent.
Authors
Elle Buser
(Emory University)
Malena Sabate Landman
(University of Oxford)
Julianne Chung
(Emory University)
Levon Nurbekyan
(Emory University)