From Ordinary Differential Equations to Structural Causal Models: the deterministic case

By Joris M. Mooij, Dominik Janzing, Bernhard Schölkopf. 2013

119 citations recorded by the source corpus.

We show how, and under which conditions, the equilibrium states of a first-order Ordinary Differential Equation (ODE) system can be described with a deterministic Structural Causal Model (SCM). Our exposition sheds more light on the concept of causality as expressed within the framework of Structural Causal Models, especially for cyclic models.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Molecular Biology, Probabilistic & Bayesian Methods, Causal Inference & Discovery

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Citations in the corpus

Toward Causal Representation Learning (2021, background): “Defining objects or variables that can be causally related amounts to coarse-graining of more detailed models of the world, including microscopic structural equation models [208], ordinary differential equations [173], [207], and temporally aggregated time series [79].”
Towards Causal Representation Learning (2021, background): “structural equation models [207], ordinary differential equations [173, 208], and temporally aggregated time series [78].”
Causality for Machine Learning (2019, background): “Some progress has been made in deriving SCMs that describe the interventional behavior of a coupled system that is in an equilibrium state and perturbed in an “adiabatic” way (Mooij et al., 2013), with generalizations to oscillatory systems (Rubenstein et al., 2018).”
From Deterministic ODEs to Dynamic Structural Causal Models (2016, methodology): “One possible way to write down an ODE is to canonically decompose it into a collection of first order differential equations, such as is done in Mooij et al. (2013).”
Causal Learning for Partially Observed Stochastic Dynamical Systems (2018, background): “Relations to structural causal models have been established for ordinary differential equations (ODEs) (Mooij et al., 2013; Rubenstein et al., 2016).”
D’ya Like DAGs? A Survey on Structure Learning and Causal Discovery (2021, background): “These include: A discussion of the relevance of causality to machine learning [71, 175, 214]; Commentaries on the nature of causality [143, 160]; alternative reviews on causal inference and causal discovery [69, 84, 92, 230, 268]; reviews with a focus on time-series causal inference and discovery [5”
UvA-DARE ( Digital Academic Repository ) Causal Consistency of Structural Equation Models (2017, unknown): “12 This interpretation corresponds to the assumption that the noise in the dynamical model is constant through time, and is used by e.g. [10, 12, 14, 15] and [13] to meaningfully interpret cyclic SEMs.”
UvA-DARE ( Digital Academic Repository ) Causal Discovery with Continuous Additive Noise Models (2014, unknown): “Under certain assumptions such as stable equilibria, one can derive an SEM that describes how the equilibrium states of such a dynamical system will react to physical interventions on the observables involved (Mooij et al., 2013).”
Reliable Decision Support using Counterfactual Models (2017, background): “The next assumption posits that the features X include all possible confounders [Morgan and Winship, 2014], which are sufficient to d-separate Y [a] and A. Assumption 2 (No Unmeasured Confounders (NUC)). Let Y be the observed outcome, A ∈ C be the observed action, X be a vector containing all potent”
Foundations of structural causal models with cycles and latent variables (2016, background): “However, causal cycles may arise when one approximates such systems over time [16, 39, 40] or when one describes the equilibrium states of these systems [3, 5, 24, 26, 30, 43, 53].”
What-If Reasoning with Counterfactual Gaussian Processes (2017, background): “Mooij et al. [2013] formalize an analog of Pearl’s “do” operation for deterministic ordinary differential equations.”
From Random Differential Equations to Structural Causal Models: the stochastic case (2018, background): “It can deal with randomness in the initial conditions, the coefficients and via the random inhomogenous part (captured as additive noise in the SCM), thereby significantly extending the work by Mooij et al. (2013) who only considers the deterministic setting.”