Causal Models for Dynamical Systems

By Jan Peters, Stefan Bauer, Niklas Pfister. 2020

58 citations recorded by the source corpus.

A probabilistic model describes a system in its observational state. In many situations, however, we are interested in the system's response under interventions. The class of structural causal models provides a language that allows us to model the behaviour under interventions. It can been taken as a starting point to answer a plethora of causal questions, including the identification of causal effects or causal structure learning. In this chapter, we provide a natural and straight-forward extension of this concept to dynamical systems, focusing on continuous time models. In particular, we introduce two types of causal kinetic models that differ in how the randomness enters into the model: it may either be considered as observational noise or as systematic driving noise. In both cases, we define interventions and therefore provide a possible starting point for causal inference. In this sense, the book chapter provides more questions than answers. The focus of the proposed causal kinetic models lies on the dynamics themselves rather than corresponding stationary distributions, for example. We believe that this is beneficial when the aim is to model the full time evolution of the system and data are measured at different time points. Under this focus, it is natural to consider interventions in the differential equations themselves.

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

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Citations in the corpus

Toward Causal Representation Learning (2021, background): “, due to unobserved confounding or a form of course graining that does not preserve the causal structure [208]), then (2) may not be causally meaningful [186], [217].”
Towards Causal Representation Learning (2021, background): “, due to unobserved confounding, or a form of course-graining that does not preserve the causal structure [207]), then (2) may not be causally meaningful [221, 190].”
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”