2020/01/17 by Jonas Peters, Peters, Jonas, Bauer, Stefan +2 · 2 citations
Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Quantum Mechanics and Applications
paper · pdf · doi:10.48550/arxiv.2001.06208
openalex publication_date 2020/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.