# From Random Differential Equations to Structural Causal Models: the stochastic case

@article{Bongers2018FromRD, title={From Random Differential Equations to Structural Causal Models: the stochastic case}, author={Stephan Bongers and Joris M. Mooij}, journal={ArXiv}, year={2018}, volume={abs/1803.08784} }

Random Differential Equations provide a natural extension of Ordinary Differential Equations to the stochastic setting. We show how, and under which conditions, every equilibrium state of a Random Differential Equation (RDE) can be described by a Structural Causal Model (SCM), while pertaining the causal semantics. This provides an SCM that captures the stochastic and causal behavior of the RDE, which can model both cycles and confounders. This enables the study of the equilibrium states of the… Expand

#### 21 Citations

From Deterministic ODEs to Dynamic Structural Causal Models

- Computer Science
- UAI
- 2018

A novel perspective on the relationship between Ordinary Differential Equations and Structural Causal Models is provided and it is shown how, under certain conditions, the asymptotic behaviour of an Ordinarydifferential Equation under non-constant interventions can be modelled using Dynamic StructuralCausal Models. Expand

From Deterministic ODEs to Dynamic Structural Causal Models

- 2018

Structural Causal Models are widely used in causal modelling, but how they relate to other modelling tools is poorly understood. In this paper we provide a novel perspective on the relationship… Expand

Beyond Structural Causal Models: Causal Constraints Models

- Computer Science
- UAI
- 2019

This work proposes a generalization of the notion of an SCM, that is called Causal Constraints Model (CCM), and proves that CCMs do capture the causal semantics of dynamical systems at equilibrium. Expand

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It is demonstrated that perfect adaptation in a simple model for a protein signalling pathway can explain why the presence and orientation of edges in the output of causal discovery algorithms does not always appear to agree with the direction of edges as the system converges to equilibrium. Expand

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- Mathematics, Computer Science
- UAI
- 2019

We prove the main rules of causal calculus (also called do-calculus) for i/o structural causal models (ioSCMs), a generalization of a recently proposed general class of non-/linear structural causal… Expand

Causal Calculus in the Presence of Cycles, Latent Confounders and Selection Bias

- 2019

We prove the main rules of causal calculus (also called do-calculus) for i/o structural causal models (ioSCMs), a generalization of a recently proposed general class of non-/linear structural causal… Expand

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This paper captures causality without reference to graphs or functional dependencies, but with information fields and Witsenhausen’s intrinsic model, and explains why, in the presence of cycles, the theory of causal inference might require different tools, depending on whether the random variables are discrete or continuous. Expand

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- NeurIPS
- 2019

It is illustrated that, in presence of Markov process model misspecification, counterfactual inference leverages prior data, and therefore estimates the outcome of an intervention more accurately than a direct simulation. Expand

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This paper gives theoretical results detailing how one can transfer interventional information across time steps and defines a dynamic causal GP model which can be used to quantify uncertainty and find optimal interventions in practice. Expand

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