Mishra Swapnil, Flaxman Seth, Berah Tresnia, Zhu Harrison, Pakkanen Mikko, Bhatt Samir
MRC Centre for Global Infectious Disease Analysis, Jameel Institute for Disease and Emergency Analytics, Imperial College London, School of Public Health, London, UK.
Section of Epidemiology, Department of Public Health, University of Copenhagen, Copenhagen, Denmark.
Stat Comput. 2022;32(6):96. doi: 10.1007/s11222-022-10151-w. Epub 2022 Oct 17.
Stochastic processes provide a mathematically elegant way to model complex data. In theory, they provide flexible priors over function classes that can encode a wide range of interesting assumptions. However, in practice efficient inference by optimisation or marginalisation is difficult, a problem further exacerbated with big data and high dimensional input spaces. We propose a novel variational autoencoder (VAE) called the prior encoding variational autoencoder ( VAE). VAE is a new continuous stochastic process. We use VAE to learn low dimensional embeddings of function classes by combining a trainable feature mapping with generative model using a VAE. We show that our framework can accurately learn expressive function classes such as Gaussian processes, but also properties of functions such as their integrals. For popular tasks, such as spatial interpolation, VAE achieves state-of-the-art performance both in terms of accuracy and computational efficiency. Perhaps most usefully, we demonstrate an elegant and scalable means of performing fully Bayesian inference for stochastic processes within probabilistic programming languages such as Stan.
随机过程为建模复杂数据提供了一种数学上优雅的方式。理论上，它们为函数类提供了灵活的先验，能够编码各种有趣的假设。然而，在实践中，通过优化或边缘化进行高效推理很困难，大数据和高维输入空间进一步加剧了这个问题。我们提出了一种新颖的变分自编码器（VAE），称为先验编码变分自编码器（Prior Encoding Variational Autoencoder，PEVAE）。PEVAE是一种新的连续随机过程。我们使用PEVAE通过将可训练特征映射与使用VAE的生成模型相结合来学习函数类的低维嵌入。我们表明，我们的框架不仅可以准确地学习诸如高斯过程等有表现力的函数类，还可以学习函数的性质，如它们的积分。对于诸如空间插值等常见任务，PEVAE在准确性和计算效率方面都达到了当前的最佳性能。也许最有用的是，我们展示了一种在诸如Stan等概率编程语言中对随机过程进行完全贝叶斯推理的优雅且可扩展的方法。
