学术报告

An Approximate Empirical Bayesian Method for Large-scale Linear-Gaussian Inverse Problems

阅读次数:1529

题目:An Approximate Empirical Bayesian Method for Large-scale Linear-Gaussian Inverse Problems

报告人:李敬来 教授 (上海交通大学)

地点:致远楼101

时间:201854日下午2:00-3:00

报告摘要:We study Bayesian inference methods for solving linear inverse problems, focusing on hierarchical formulations where the prior or the likelihood function depend on unspecified hyperparameters. In practice, these hyperparameters are often determined via an empirical Bayesian method that maximizes the marginal likelihood function, i.e., the probability density of the data conditional on the hyperparameters. Evaluating the marginal likelihood, however, is computationally challenging for large- scale problems. In this work, we present a method to approximately evaluate marginal likelihood functions, based on a low-rank approximation of the update from the prior covariance to the posterior covariance. We show that this approximation is optimal in a minimax sense. Moreover, we provide an efficient algorithm to implement the proposed method, based on a combination of the randomized SVD and a spectral approximation method to compute square roots of the prior covariance matrix. Several numerical examples demonstrate good performance of the proposed method.

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