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，但若假设原始变量由独立的潜在分量生成，则可简化此过程。若能找到这些分量，则可对其进行单变量建模。盲源分离旨在仅基于观测数据估计解混变换，从而恢复潜在分量。现有的时空盲源分离方法局限于线性解混，其非线性变体尚未实现。本文扩展了可识别变分自编码器，将其应用于非线性非平稳时空盲源分离场景，并通过全面的仿真研究验证了其性能。此外，我们引入了两种替代方法用于潜在维度估计，这是获得正确潜在表示的关键步骤。最后，我们通过一个气象学应用实例对所提方法进行了说明：在该应用中，我们估计了潜在维度和潜在分量，解释了各分量的含义，并展示了如何将所提出的非线性盲源分离方法作为预处理步骤，以考虑非平稳性并提高预测精度。