Modelling multivariate spatio-temporal data with identifiable variational autoencoders.

Area of Science:

• Statistics
• Machine Learning
• Data Science

Background:

• Modeling complex spatio-temporal data presents significant challenges due to intricate dependency structures.
• Simplifying these models can be achieved by assuming data originates from independent latent components.
• Blind source separation (BSS) aims to recover these latent components by estimating the unmixing transformation from observed data.

Purpose of the Study:

• To extend identifiable variational autoencoders to nonlinear, nonstationary spatio-temporal blind source separation.
• To introduce novel methods for latent dimension estimation crucial for accurate latent representation.
• To demonstrate the practical utility of the proposed methods in meteorological data analysis.

Main Methods:

• Extension of identifiable variational autoencoders for nonlinear, nonstationary spatio-temporal BSS.
• Development of two alternative techniques for latent dimension estimation.
• Application and validation through comprehensive simulation studies and a meteorological case study.

Main Results:

• The proposed method effectively performs nonlinear, nonstationary spatio-temporal blind source separation.
• The introduced latent dimension estimation techniques provide accurate latent representations.
• The method successfully accounts for nonstationarity and enhances prediction accuracy in meteorological applications.

Conclusions:

• The developed nonlinear BSS approach offers a powerful tool for analyzing complex spatio-temporal data.
• Accurate latent dimension estimation is vital for successful component recovery.
• The method demonstrates potential for improving forecasting and understanding in fields like meteorology.