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

arXiv: https://arxiv.org/abs/2509.11962 · HTML: https://mlsanity.com/paper/2509.11962/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 26 references that are in the map.
- First posted on arXiv 15 Sep 2025.

## Builds on (most cited first, 9 of 9)

- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning](https://mlsanity.com/paper/1805.08651/) (2018)
- [Unsupervised Feature Extraction by Time-Contrastive Learning and Nonlinear ICA](https://mlsanity.com/paper/1605.06336/) (2016)
- [Disentanglement via Mechanism Sparsity Regularization: A New Principle for Nonlinear ICA](https://mlsanity.com/paper/2107.10098/) (2021)
- [Hidden Markov Nonlinear ICA: Unsupervised Learning from Nonstationary Time Series](https://mlsanity.com/paper/2006.12107/) (2020)
- [Nonlinear Independent Component Analysis for Principled Disentanglement in Unsupervised Deep Learning](https://mlsanity.com/paper/2303.16535/) (2023)
- [Modelling multivariate spatio-temporal data with identifiable variational autoencoders](https://mlsanity.com/paper/2409.04162/) (2024)
- [Stationary subspace analysis based on second-order statistics](https://mlsanity.com/paper/2103.06148/) (2021)
- [Nonlinear blind source separation exploiting spatial nonstationarity](https://mlsanity.com/paper/2311.08004/) (2023)

## Built on by (most cited first, 1 of 1)

- [AR-Flow VAE: A Structured Autoregressive Flow Prior Variational Autoencoder for Unsupervised Blind Source Separation](https://mlsanity.com/paper/2603.14441/) (2026)

## Abstract (arXiv)

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.