Causal interpretation of stochastic differential equations

By Alexander Sokol, Niels Richard Hansen. 2013

61 citations recorded by the source corpus.

We give a causal interpretation of stochastic differential equations (SDEs) by defining the postintervention SDE resulting from an intervention in an SDE. We show that under Lipschitz conditions, the solution to the postintervention SDE is equal to a uniform limit in probability of postintervention structural equation models based on the Euler scheme of the original SDE, thus relating our definition to mainstream causal concepts. We prove that when the driving noise in the SDE is a Levy process, the postintervention distribution is identifiable from the generator of the SDE.

Subfields: Artificial Intelligence, Molecular Biology, Statistics and Probability, Probabilistic & Bayesian Methods, Causal Inference & Discovery

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Citations in the corpus

From Deterministic ODEs to Dynamic Structural Causal Models (2016, background): “…from more fundamental models by showing how, under strong assumptions, SCMs can be derived from an underlying discrete time difference equation or continuous time ODE (Iwasaki and Simon, 1994; Dash, 2005; Lacerda et al., 2008; Voortman et al., 2010; Mooij et al., 2013; Sokol and Hansen, 2014).”
Can we believe the DAGs? A comment on the relationship between causal DAGs and mechanisms (2014, unknown): “2014–5:14pm] [1–21] //blrnas3/cenpro/ApplicationFiles/Journals/SAGE/3B2/SMMJ/Vol00000/130248/APPFile/SG-SMMJ130248.”
Causal Learning for Partially Observed Stochastic Dynamical Systems (2018, methodology): “Sokol and Hansen (2015) for details and weak conditions ensuring that (2) holds.”
Identifying Causal Structure in Large-Scale Kinetic Systems (2018, background): “Nevertheless, interventions of the form Xkt := ζ(X A t ) with A ⊆ {1, . . . , d} \ {k} [e.g. Hansen and Sokol, 2014], and Xkt := ζ(t) [e.g. Rubenstein et al., 2018] are included in our formalism as well.”
What-If Reasoning with Counterfactual Gaussian Processes (2017, background): “Sokol and Hansen [2014] make similar contributions for stochastic differential equations by studying limits of discrete-time non-parametric structural equation models [Pearl, 2009].”
Markov equivalence of marginalized local independence graphs (2018, background): “We will not go into a full discussion of how to formalize “inﬂuence” in terms of a continuous-time causal dynamical model as this would lead us astray; see instead [13, 27, 38].”
From Random Differential Equations to Structural Causal Models: the stochastic case (2018, background): “Earlier work has shown that SCMs can be derived from stochastic differential equations (Hansen and Sokol, 2014), however they restrict to the acyclic case.”