提出一种高效采样框架，统一解决贝叶斯成像中的先验与后验采样问题。
The Gaussian Latent Machine: Efficient Prior and Posterior Sampling for Inverse Problems
- 构建高斯隐变量模型，将复杂分布转化为可高效采样的结构。
- 通用情况下实现两块吉布斯采样，效率显著优于传统方法。
- 适用于多种成像任务，尤其适合需要快速采样的实际应用。
我们研究了从一类乘积专家型模型中采样的问题，该模型涵盖贝叶斯成像中常见的多种标准先验与后验分布。本文证明该模型可被轻松提升为一种新型隐变量模型，称为高斯隐变量机（Gaussian latent machine）。这一转换带来了一种通用的采样方法，统一并推广了文献中许多已有算法。最显著的是，在一般情况下，该方法实现了高效且有效的两块吉布斯采样；在特定情形下，则退化为直接采样算法。最后，通过详尽的数值实验，验证了所提采样方法在各类贝叶斯成像先验与后验采样问题上的高效性与有效性。
原文摘要 · Abstract (English)
We consider the problem of sampling from a product-of-experts-type model that encompasses many standard prior and posterior distributions commonly found in Bayesian imaging. We show that this model can be easily lifted into a novel latent variable model, which we refer to as a Gaussian latent machine. This leads to a general sampling approach that unifies and generalizes many existing sampling algorithms in the literature. Most notably, it yields a highly efficient and effective two-block Gibbs sampling approach in the general case, while also specializing to direct sampling algorithms in particular cases. Finally, we present detailed numerical experiments that demonstrate the efficiency and effectiveness of our proposed sampling approach across a wide range of prior and posterior sampling problems from Bayesian imaging.
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