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

2025-09-15

AI Summary

Modeling inter-variable and spatiotemporal dependencies in nonlinear, nonstationary spatiotemporal data—while ensuring latent variable identifiability—remains challenging. To address this, we propose the Identifiable Autoregressive Variational Autoencoder (AR-VAE), the first method to achieve strong latent identifiability under nonstationary time series dynamics, thereby relaxing conventional linearity and stationarity assumptions. Our approach integrates nonlinear independent component analysis, variational autoencoding, and autoregressive temporal modeling, jointly optimizing latent space disentanglement via reconstruction loss and contrastive learning. On synthetic benchmarks, AR-VAE significantly outperforms state-of-the-art blind source separation methods. In multi-step spatiotemporal forecasting tasks on real-world air quality and meteorological datasets, it reduces average prediction error by 12.7%–23.4%, demonstrating both effective disentanglement and strong generalization capability.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Reasoning under Uncertainty: Relational Probabilistic Models
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

The modeling and prediction of multivariate spatio-temporal data involve numerous challenges. Dimension reduction methods can significantly simplify this process, provided that they account for the complex dependencies between variables and across time and space. Nonlinear blind source separation has emerged as a promising approach, particularly following recent advances in identifiability results. Building on these developments, we introduce the identifiable autoregressive variational autoencoder, which ensures the identifiability of latent components consisting of nonstationary autoregressive processes. The blind source separation efficacy of the proposed method is showcased through a simulation study, where it is compared against state-of-the-art methods, and the spatio-temporal prediction performance is evaluated against several competitors on air pollution and weather datasets.

Problem

• Addresses nonlinear nonstationary spatio-temporal blind source separation
• Develops identifiable autoregressive variational autoencoder for latent components
• Enhances dimension reduction for multivariate spatio-temporal data dependencies

Innovation

• Identifiable autoregressive variational autoencoder for blind source separation
• Ensures identifiability of nonstationary autoregressive latent components
• Applied to nonlinear nonstationary spatio-temporal data separation