# Variational System Identification for Nonlinear State-Space Models

arXiv: https://arxiv.org/abs/2012.05072 · HTML: https://mlsanity.com/paper/2012.05072/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Dec 2020.

## Built on by (most cited first, 4 of 4)

- [Ensemble Kalman Filtering Meets Gaussian Process SSM for Non-Mean-Field and Online Inference](https://mlsanity.com/paper/2312.05910/) (2023)
- [Learning Surrogate LPV State-Space Models with Uncertainty Quantification](https://mlsanity.com/paper/2603.29532/) (2026)
- [Nonlinear Bayesian Estimator for Parameter Learning: A Fixed-Point Characterization](https://mlsanity.com/paper/2606.10111/) (2026)
- [PR-Smoother: Simulator-Preserving Non-Gaussian Smoothing for Data Assimilation](https://mlsanity.com/paper/2609.26890/) (2026)

## Abstract (arXiv)

This paper considers parameter estimation for nonlinear state-space models, which is an important but challenging problem. We address this challenge by employing a variational inference (VI) approach, which is a principled method that has deep connections to maximum likelihood estimation. This VI approach ultimately provides estimates of the model as solutions to an optimisation problem, which is deterministic, tractable and can be solved using standard optimisation tools. A specialisation of this approach for systems with additive Gaussian noise is also detailed. The proposed method is examined numerically on a range of simulated and real examples focusing on the robustness to parameter initialisation; additionally, favourable comparisons are performed against state-of-the-art alternatives.