# Cyclic Causal Discovery from Continuous Equilibrium Data

arXiv: https://arxiv.org/abs/1309.6849 · HTML: https://mlsanity.com/paper/1309.6849/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Sep 2013.

## Built on by (most cited first, 21 of 21)

- [Interventional Causal Representation Learning](https://mlsanity.com/paper/2209.11924/) (2022)
- [NODAGS-Flow: Nonlinear Cyclic Causal Structure Learning](https://mlsanity.com/paper/2301.01849/) (2023)
- [Causal Modeling with Stationary Diffusions](https://mlsanity.com/paper/2310.17405/) (2023)
- [Characterization and Greedy Learning of Gaussian Structural Causal Models under Unknown Interventions](https://mlsanity.com/paper/2211.14897/) (2022)
- [Incorporating Causal Graphical Prior Knowledge into Predictive Modeling via Simple Data Augmentation](https://mlsanity.com/paper/2103.00136/) (2021)
- [Obtaining Causal Information by Merging Datasets with MAXENT](https://mlsanity.com/paper/2107.07640/) (2021)
- [Towards a Grounded Theory of Causation for Embodied AI](https://mlsanity.com/paper/2206.13973/) (2022)
- [Local Causal Discovery with Linear non-Gaussian Cyclic Models](https://mlsanity.com/paper/2403.14843/) (2024)
- [Establishing Markov Equivalence in Cyclic Directed Graphs](https://mlsanity.com/paper/2309.03092/) (2023)
- [A Fast Non-parametric Approach for Local Causal Structure Learning](https://mlsanity.com/paper/2111.14969/) (2021)
- [Efficient Ensemble Conditional Independence Test Framework for Causal Discovery](https://mlsanity.com/paper/2509.21021/) (2025)
- [Causality and independence in perfectly adapted dynamical systems](https://mlsanity.com/paper/2101.11885/) (2021)
- [Directed Cyclic Graph for Causal Discovery from Multivariate Functional Data](https://mlsanity.com/paper/2310.20537/) (2023)
- [Differentiable Cyclic Causal Discovery Under Unmeasured Confounders](https://mlsanity.com/paper/2508.08450/) (2025)
- [Learning Cyclic Causal Models from Incomplete Data](https://mlsanity.com/paper/2402.15625/) (2024)
- [MissNODAG: Differentiable Cyclic Causal Graph Learning from Incomplete Data](https://mlsanity.com/paper/2410.18918/) (2024)
- [Measure-Theoretic Probability of Complex Co-occurrence and E-Integral](https://mlsanity.com/paper/2210.09913/) (2022)
- [Linear Causal Discovery with Interventional Constraints](https://mlsanity.com/paper/2510.26342/) (2025)
- [Causality-Encoded Diffusion Models for Interventional Sampling and Edge Inference](https://mlsanity.com/paper/2604.21843/) (2026)
- [SCOUT: Cyclic Causal Discovery Under Soft Interventions with Unknown Targets](https://mlsanity.com/paper/2605.16620/) (2026)
- [Reconciling Causality and Non-Equilibrium Thermodynamics with Hamiltonian Causal Models](https://mlsanity.com/paper/2606.04822/) (2026)

## Abstract (arXiv)

We propose a method for learning cyclic causal models from a combination of observational and interventional equilibrium data. Novel aspects of the proposed method are its ability to work with continuous data (without assuming linearity) and to deal with feedback loops. Within the context of biochemical reactions, we also propose a novel way of modeling interventions that modify the activity of compounds instead of their abundance. For computational reasons, we approximate the nonlinear causal mechanisms by (coupled) local linearizations, one for each experimental condition. We apply the method to reconstruct a cellular signaling network from the flow cytometry data measured by Sachs et al. (2005). We show that our method finds evidence in the data for feedback loops and that it gives a more accurate quantitative description of the data at comparable model complexity.