Reconciling "priors" & "priors" without prejudice?
Reconciling "priors" & "priors" without prejudice?
复制标题
调和“先验”
DOI：
--
复制
发表时间：
2013
期刊：
影响因子：
--
通讯作者：
Pierre Machart
中科院分区：
文献类型：
--
作者：
R. Gribonval;Pierre Machart
有两个主要的路线来解决线性逆问题。而基于正则化的方法建立估计作为惩罚回归优化问题的解决方案，贝叶斯估计依赖于未知的后验分布，给定一些假设的先验族。虽然这些方法可能看起来完全不同，但最近的结果表明，在加性白色高斯去噪的背景下，贝叶斯条件均值估计总是惩罚回归问题的解决方案。本文的贡献是双重的。首先，我们将加性白色高斯去噪的结果推广到一般的有色高斯噪声线性逆问题。其次，我们刻画了条件下的罚函数与条件均值估计可以满足某些流行的性质，如凸性，可分性和光滑性。这揭示了稀疏正则化中计算效率和估计精度之间的一些权衡，并在贝叶斯估计和近似优化之间建立了一些联系。
There are two major routes to address linear inverse problems. Whereas regularization-based approaches build estimators as solutions of penalized regression optimization problems, Bayesian estimators rely on the posterior distribution of the unknown, given some assumed family of priors. While these may seem radically different approaches, recent results have shown that, in the context of additive white Gaussian denoising, the Bayesian conditional mean estimator is always the solution of a penalized regression problem. The contribution of this paper is twofold. First, we extend the additive white Gaussian denoising results to general linear inverse problems with colored Gaussian noise. Second, we characterize conditions under which the penalty function associated to the conditional mean estimator can satisfy certain popular properties such as convexity, separability, and smoothness. This sheds light on some tradeoff between computational efficiency and estimation accuracy in sparse regularization, and draws some connections between Bayesian estimation and proximal optimization.
影响因子：
2.5
作者：
Gribonval, Remi;Cevher, Volkan;Davies, Mike E.
通讯作者：
Davies, Mike E.