Modelling multivariate spatio-temporal data with complex dependency structures is a challenging task but can be simplified by assuming that the original variables are generated from independent latent components. If these components are found, they can be modelled univariately. Blind source separation aims to recover the latent components by estimating the unmixing transformation based on the observed data only. The current methods for spatio-temporal blind source separation are restricted to linear unmixing, and nonlinear variants have not been implemented. In this paper, we extend identifiable variational autoencoder to the nonlinear nonstationary spatio-temporal blind source separation setting and demonstrate its performance using comprehensive simulation studies. Additionally, we introduce two alternative methods for the latent dimension estimation, which is a crucial task in order to obtain the correct latent representation. Finally, we illustrate the proposed methods using a meteorological application, where we estimate the latent dimension and the latent components, interpret the components, and show how nonstationarity can be accounted and prediction accuracy can be improved by using the proposed nonlinear blind source separation method as a preprocessing method.

翻译：对具有复杂依赖结构的多元时空数据进行建模是一项具有挑战性的任务，但可以通过假设原始变量由独立的潜在分量生成来简化。如果能够找到这些分量，便可以对它们进行单变量建模。盲源分离旨在仅基于观测数据估计解混变换，以恢复潜在分量。当前针对时空盲源分离的方法仅限于线性解混，非线性变体尚未实现。本文中，我们将可识别变分自编码器扩展到非线性非平稳时空盲源分离场景，并通过全面的仿真研究展示了其性能。此外，我们引入了两种用于潜在维度估计的替代方法，这是获得正确潜在表示的关键任务。最后，我们通过一个气象学应用对所提出的方法进行了说明，其中我们估计了潜在维度和潜在分量，解释了这些分量，并展示了如何通过使用所提出的非线性盲源分离方法作为预处理方法来考虑非平稳性并提高预测精度。