# Graphical continuous Lyapunov models

arXiv: https://arxiv.org/abs/2005.10483 · HTML: https://mlsanity.com/paper/2005.10483/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 May 2020.

## Built on by (most cited first, 9 of 9)

- [Discovering Causal Relations and Equations from Data](https://mlsanity.com/paper/2305.13341/) (2023)
- [Causal Modeling with Stationary Diffusions](https://mlsanity.com/paper/2310.17405/) (2023)
- [On the Parameter Identifiability of Partially Observed Linear Causal Models](https://mlsanity.com/paper/2407.16975/) (2024)
- [Joint trajectory and network inference via reference fitting](https://mlsanity.com/paper/2409.06879/) (2024)
- [Efficient Learning of Stationary Diffusions with Stein-type Discrepancies](https://mlsanity.com/paper/2601.16597/) (2026)
- [Coarsening Linear Non-Gaussian Causal Models with Cycles](https://mlsanity.com/paper/2605.10163/) (2026)
- [Towards Identifiability of Interventional Stochastic Differential Equations](https://mlsanity.com/paper/2505.15987/) (2025)
- [Sign Identifiability of Causal Effects in Stationary Stochastic Dynamical Systems](https://mlsanity.com/paper/2603.08311/) (2026)
- [Non-parametric recovery of causal diffusion mechanisms from steady-state observations](https://mlsanity.com/paper/2606.30467/) (2026)

## Abstract (arXiv)

The linear Lyapunov equation of a covariance matrix parametrizes the equilibrium covariance matrix of a stochastic process. This parametrization can be interpreted as a new graphical model class, and we show how the model class behaves under marginalization and introduce a method for structure learning via ℓ1-penalized loss minimization. Our proposed method is demonstrated to outperform alternative structure learning algorithms in a simulation study, and we illustrate its application for protein phosphorylation network reconstruction.