Identifiable Autoregressive Variational Autoencoders for Nonlinear and Nonstationary Spatio-Temporal Blind Source Separation

This chapter delves into the development and application of identifiable autoregressive variational autoencoders (iVAEar) for nonlinear and nonstationary spatio-temporal blind source separation. The text begins by introducing the challenges and complexities of modeling and predicting multivariate spatio-temporal data, highlighting the need for advanced techniques that can handle nonstationary data without restrictive assumptions. The authors present the iVAEar method, which extends identifiability to cases with nonstationary autoregressive coefficients, a significant improvement over previous methods. The chapter includes a detailed discussion on the model assumptions, identifiability conditions, and the estimation method for the iVAEar model. Comprehensive simulation studies are conducted to compare the performance of iVAEar against other state-of-the-art methods, demonstrating its superior accuracy in various scenarios. Additionally, the text explores the application of iVAEar to real-world datasets, such as air pollution and weather measurements, showcasing its potential for improved multivariate spatio-temporal prediction. The chapter concludes with a discussion on the limitations and future directions for research, emphasizing the need for extensions to nonseparable models and more general graph-structured data. Overall, this chapter provides a thorough exploration of iVAEar, offering valuable insights and practical applications for professionals in the field of machine learning and data analysis.