分析生成先验在贝叶斯反问题中的误差，给出可量化边界。
Error Analysis of Bayesian Inverse Problems with Generative Priors
- 基于Wasserstein-2最小化生成模型构建先验
- 后验误差率与先验的Wasserstein-1距离一致
- 适用于非平稳场建模的反问题研究
近年来，得益于机器学习技术的发展，数据驱动的反问题求解方法日益流行。一种常见做法是利用额外数据训练生成模型，以学习针对具体问题的定制化先验。本文对这类问题进行了分析，给出了最小Wasserstein-2生成模型作为先验时的定量误差界。在一定假设下，我们证明后验误差的收敛速率与先验在Wasserstein-1距离下的误差率相同。进一步通过数值实验验证了误差分析在多个基准测试中的表现，并以椭圆型偏微分方程反问题为例，展示了生成先验在建模非平稳场中的应用效果。
原文摘要 · Abstract (English)
Data-driven methods for the solution of inverse problems have become widely popular in recent years thanks to the rise of machine learning techniques. A popular approach concerns the training of a generative model on additional data to learn a bespoke prior for the problem at hand. In this article we present an analysis for such problems by presenting quantitative error bounds for minimum Wasserstein-2 generative models for the prior. We show that under some assumptions, the error in the posterior due to the generative prior will inherit the same rate as the prior with respect to the Wasserstein-1 distance. We further present numerical experiments that verify that aspects of our error analysis manifests in some benchmarks followed by an elliptic PDE inverse problem where a generative prior is used to model a non-stationary field.
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