In applied fields where the speed of inference and model flexibility are crucial, the use of Bayesian inference for models with a stochastic process as their prior, e.g. Gaussian processes (GPs) is ubiquitous. Recent literature has demonstrated that the computational bottleneck caused by GP priors or their finite realizations can be encoded using deep generative models such as variational autoencoders (VAEs), and the learned generators can then be used instead of the original priors during Markov chain Monte Carlo (MCMC) inference in a drop-in manner. While this approach enables fast and highly efficient inference, it loses information about the stochastic process hyperparameters, and, as a consequence, makes inference over hyperparameters impossible and the learned priors indistinct. We propose to resolve the aforementioned issue and disentangle the learned priors by conditioning the VAE on stochastic process hyperparameters. This way, the hyperparameters are encoded alongside GP realisations and can be explicitly estimated at the inference stage. We believe that the new method, termed PriorCVAE, will be a useful tool among approximate inference approaches and has the potential to have a large impact on spatial and spatiotemporal inference in crucial real-life applications. Code showcasing the PriorCVAE technique can be accessed via the following link: https://github.com/elizavetasemenova/PriorCVAE

翻译：在推理速度与模型灵活性至关重要的应用领域，使用以随机过程为先验（例如高斯过程）的贝叶斯推断模型已十分普遍。近期文献表明，由高斯过程先验或其有限实现导致的计算瓶颈可通过深度生成模型（如变分自编码器）进行编码，并在马尔可夫链蒙特卡洛推断中以即插即用的方式替代原始先验使用学得的生成器。尽管该方法能够实现快速高效的推断，但会丢失关于随机过程超参数的信息，从而导致无法对超参数进行推断，且学得的先验变得模糊不清。我们提出通过以随机过程超参数为条件对变分自编码器进行约束，从而解决上述问题并解耦学得的先验。这样，超参数将与高斯过程实现一同被编码，并在推断阶段进行显式估计。我们相信，这种名为PriorCVAE的新方法将成为近似推断方法中的有用工具，并有望在关键实际应用中对空间及时空推断产生重大影响。PriorCVAE技术的代码可通过以下链接获取：https://github.com/elizavetasemenova/PriorCVAE