Recent advances have shown that GP priors, or their finite realisations, can be encoded using deep generative models such as variational autoencoders (VAEs). These learned generators can serve as drop-in replacements for the original priors during MCMC inference. While this approach enables efficient inference, it loses information about the hyperparameters of the original models, and consequently makes inference over hyperparameters impossible and the learned priors indistinct. To overcome this limitation, we condition the VAE on stochastic process hyperparameters. This allows the joint encoding of hyperparameters with GP realizations and their subsequent estimation during inference. Further, we demonstrate that our proposed method, PriorCVAE, is agnostic to the nature of the models which it approximates, and can be used, for instance, to encode solutions of ODEs. It provides a practical tool for approximate inference and shows potential in real-life spatial and spatiotemporal applications.

翻译：近期研究表明，高斯过程先验或其有限实现可通过深度生成模型（如变分自编码器）进行编码。这些学习得到的生成器可在MCMC推断中替代原始先验。尽管该方法实现了高效推断，但它丢失了原始模型的超参数信息，导致无法对超参数进行推断且学习到的先验不明确。为克服这一局限，我们将VAE以随机过程超参数为条件，从而实现对超参数与高斯过程实现的联合编码，并在推断过程中对其进行后续估计。此外，我们证明所提出的PriorCVAE方法对所近似模型的类型具有无关性，例如可用于编码常微分方程的解。该方法为近似推断提供了实用工具，并在实际空间及时空应用中展现出潜力。