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Dynamic Structural Causal Models
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We study a specific type of SCM, called a Dynamic Structural Causal Model (DSCM), whose endogenous variables represent functions of time, which is possibly cyclic and allows for latent confounding. As a motivating use-case, we show that certain systems of Stochastic Differential Equations (SDEs) can be appropriately represented with DSCMs. An immediate consequence of this construction is a graphical Markov property for systems of SDEs. We define a time-splitting operation, allowing us to analyse the concept of local independence (a notion of continuous-time Granger (non-)causality). We also define a subsampling operation, which returns a discrete-time DSCM, and which can be used for mathematical analysis of subsampled time-series. We give suggestions how DSCMs can be used for identification of the causal effect of time-dependent interventions, and how existing constraint-based causal discovery algorithms can be applied to time-series data.
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Cited by 2 Pith papers
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Orca: Neural Operators for Causal Reasoning in Continuous Time
Orca extends structural causal models to continuous time with neural operators, enabling resolution-invariant dose-response and counterfactual trajectories on irregularly sampled cyclic systems.
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Deep Koopman operator framework for causal discovery in nonlinear dynamical systems
A deep Koopman framework called Kausal discovers causal direction and magnitude in nonlinear dynamical systems by comparing joint versus marginal prediction errors in learned observable spaces.
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