Nonlinear blind source separation for spatio-temporal data
Conference
65th ISI World Statistics Congress 2025
Format: IPS Abstract - WSC 2025
Keywords: dimension-reduction, dimensionreduction, nonlinear, spatio-temporal analysis
Session: IPS 914 - Recent Advances on High-Dimensional Statistics for Complex Data
Tuesday 7 October 10:50 a.m. - 12:30 p.m. (Europe/Amsterdam)
Abstract
Modeling multivariate spatio-temporal data with complex dependency structures presents significant challenges. Simplifications can be achieved by assuming that the observed variables are manifestations of independent latent components. Once these components are identified, they can be modeled univariately. Blind Source Separation (BSS) techniques aim to recover these latent components by estimating an unmixing transformation based solely on the observed data. However, current methods for spatio-temporal BSS are limited to linear transformations, and nonlinear extensions have yet to be developed. In this paper, we adapt the identifiable Variational Autoencoder (iVAE) to the nonlinear, nonstationary spatio-temporal BSS context, and evaluate its effectiveness through extensive simulation studies. We also introduce two novel methods for estimating the latent dimension, a critical step for accurate latent representation. We apply our proposed methods to a meteorological dataset, estimating its latent dimension and components, interpreting these components, and demonstrating how our nonlinear BSS approach can accommodate nonstationarity and enhance predictive accuracy when used as a preprocessing tool.