# Identifiability Analysis of Linear ODE Systems with Hidden Confounders

arXiv: https://arxiv.org/abs/2410.21917 · HTML: https://mlsanity.com/paper/2410.21917/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 47 references that are in the map.
- First posted on arXiv 29 Oct 2024.

## Builds on (most cited first, 13 of 13)

- [Symplectic ODE-Net: Learning Hamiltonian Dynamics with Control](https://mlsanity.com/paper/1909.12077/) (2019)
- [Linear Causal Disentanglement via Interventions](https://mlsanity.com/paper/2211.16467/) (2022)
- [Causal Networks: Semantics and Expressiveness](https://mlsanity.com/paper/1304.2379/) (2013)
- [Latent Hierarchical Causal Structure Discovery with Rank Constraints](https://mlsanity.com/paper/2210.01798/) (2022)
- [Neural graphical modelling in continuous-time: consistency guarantees and algorithms](https://mlsanity.com/paper/2105.02522/) (2021)
- [From Ordinary Differential Equations to Structural Causal Models: the deterministic case](https://mlsanity.com/paper/1408.2063/) (2014)
- [From Deterministic ODEs to Dynamic Structural Causal Models](https://mlsanity.com/paper/1608.08028/) (2016)
- [Beyond Predictions in Neural ODEs: Identification and Interventions](https://mlsanity.com/paper/2106.12430/) (2021)
- [Identifiability Analysis of Linear Ordinary Differential Equation Systems with a Single Trajectory](https://mlsanity.com/paper/2103.05660/) (2021)
- [Sparsity in Continuous-Depth Neural Networks](https://mlsanity.com/paper/2210.14672/) (2022)
- [Identifiability and Asymptotics in Learning Homogeneous Linear ODE Systems from Discrete Observations](https://mlsanity.com/paper/2210.05955/) (2022)
- [FRITL: A Hybrid Method for Causal Discovery in the Presence of Latent Confounders](https://mlsanity.com/paper/2103.14238/) (2021)
- [Generator Identification for Linear SDEs with Additive and Multiplicative Noise](https://mlsanity.com/paper/2310.19491/) (2023)

## Built on by (most cited first, 5 of 5)

- [Identifiability Challenges in Sparse Linear Ordinary Differential Equations](https://mlsanity.com/paper/2506.09816/) (2025)
- [Physics from Video: Identifiability of Time-Invariant Second-Order ODEs under Minimal Trajectory Conditions](https://mlsanity.com/paper/2606.00115/) (2026)
- [Limits of Learning Linear Dynamics from Experiments](https://mlsanity.com/paper/2605.12010/) (2026)
- [One Intervention per Component is Enough: Towards Identifiability in Linear Stochastic Dynamics from Steady State](https://mlsanity.com/paper/2609.19955/) (2026)
- [Identifying ODEs from Unstructured Data with Causal Representation Learning](https://mlsanity.com/paper/2609.37083/) (2026)

## Abstract (arXiv)

The identifiability analysis of linear Ordinary Differential Equation (ODE) systems is a necessary prerequisite for making reliable causal inferences about these systems. While identifiability has been well studied in scenarios where the system is fully observable, the conditions for identifiability remain unexplored when latent variables interact with the system. This paper aims to address this gap by presenting a systematic analysis of identifiability in linear ODE systems incorporating hidden confounders. Specifically, we investigate two cases of such systems. In the first case, latent confounders exhibit no causal relationships, yet their evolution adheres to specific functional forms, such as polynomial functions of time t. Subsequently, we extend this analysis to encompass scenarios where hidden confounders exhibit causal dependencies, with the causal structure of latent variables described by a Directed Acyclic Graph (DAG). The second case represents a more intricate variation of the first case, prompting a more comprehensive identifiability analysis. Accordingly, we conduct detailed identifiability analyses of the second system under various observation conditions, including both continuous and discrete observations from single or multiple trajectories. To validate our theoretical results, we perform a series of simulations, which support and substantiate our findings.