用扩散模型模拟非平稳高斯过程的后验采样，提升气候数据预测精度。
Predictive posterior sampling from non-stationnary Gaussian process priors via Diffusion models with application to climate data
- 用扩散模型替代非平稳高斯过程先验，构建可采样的代理模型
- 训练后无需微调即可生成接近真实后验的分布，统计指标验证有效
- 适用于环境科学中的反问题求解，适合做不确定性建模的研究者
基于高斯过程（GP）的贝叶斯模型能灵活预测空间分布变量并量化不确定性。但非平稳先验常需捕捉复杂空间模式，导致预测后验分布（PPD）采样计算上不可行。本文提出一种两阶段方法：首先用扩散生成模型（DGM）替代GP先验，再利用近期无训练指导算法从目标后验中采样。我们在一个复杂的非平稳GP先验上应用该方法，其精确后验采样不可行，验证显示生成分布与真实GP后验在多个统计指标上接近。此外，我们演示了如何微调训练好的DGM以聚焦特定先验区域。最后将该方法应用于环境科学中的反问题，实现当前最优预测性能。
原文摘要 · Abstract (English)
Bayesian models based on Gaussian processes (GPs) offer a flexible framework to predict spatially distributed variables with uncertainty. But the use of nonstationary priors, often necessary for capturing complex spatial patterns, makes sampling from the predictive posterior distribution (PPD) computationally intractable. In this paper, we propose a two-step approach based on diffusion generative models (DGMs) to mimic PPDs associated with non-stationary GP priors: we replace the GP prior by a DGM surrogate, and leverage recent advances on training-free guidance algorithms for DGMs to sample from the desired posterior distribution. We apply our approach to a rich non-stationary GP prior from which exact posterior sampling is untractable and validate that the issuing distributions are close to their GP counterpart using several statistical metrics. We also demonstrate how one can fine-tune the trained DGMs to target specific parts of the GP prior. Finally we apply the proposed approach to solve inverse problems arising in environmental sciences, thus yielding state-of-the-art predictions.
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