From Deterministic ODEs to Dynamic Structural Causal Models

By Paul K. Rubenstein, Stephan Bongers, Joris M. Mooij, Bernhard Schölkopf. 2016

63 citations recorded by the source corpus.

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 between Ordinary Differential Equations and Structural Causal Models. We show how, under certain conditions, the asymptotic behaviour of an Ordinary Differential Equation under non-constant interventions can be modelled using Dynamic Structural Causal Models. In contrast to earlier work, we study not only the effect of interventions on equilibrium states; rather, we model asymptotic behaviour that is dynamic under interventions that vary in time, and include as a special case the study of static equilibria.

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

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Bernhard Schölkopf
2. Yoshua Bengio
3. Anirudh Goyal
4. Stefan Bauer
5. Jan Peters
6. Sergey Levine
7. Nan Rosemary Ke
8. Francesco Locatello

In Statistics and Probability

1. Bernhard Schölkopf
2. Jan Peters
3. Joris M. Mooij
4. Stefan Bauer
5. Niklas Pfister
6. Anirudh Goyal
7. Yoshua Bengio
8. Francesco Locatello

In Probabilistic & Bayesian Methods

1. Bernhard Schölkopf
2. Yoshua Bengio
3. Anirudh Goyal
4. Jan Peters
5. Stefan Bauer
6. Francesco Locatello
7. Joris M. Mooij
8. Stephan Bongers

In Causal Inference & Discovery

1. Bernhard Schölkopf
2. Stefan Bauer
3. Jan Peters
4. Yoshua Bengio
5. Anirudh Goyal
6. Joris M. Mooij
7. Dominik Janzing
8. Nan Rosemary Ke

Citations in the corpus

• Towards Causal Representation Learning (2021, background): “structural equation models [207], ordinary differential equations [173, 208], and temporally aggregated time series [78].”
• Causal Models for Dynamical Systems (2020, background): “Nevertheless, for a differentiable ζ , interventions of the form Hansen and Sokol, 2014], and Rubenstein et al., 2018] are included in the above formalism as well.”
• Causality for Machine Learning (2019, background): “, 2013), with generalizations to oscillatory systems (Rubenstein et al., 2018).”
• 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).”
• From Random Differential Equations to Structural Causal Models: the stochastic case (2018, background): “Recent work has shown that dynamic asymptotic behaviour of ordinary differential equations can be captured by dynamic structural causal models (Rubenstein et al., 2016).”
• 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.”