Parameter estimation for dynamic structural causal models

Develop methods for estimating the parameters of Dynamic Structural Causal Models from data, motivated by the complexity of the model derived for the simple harmonic oscillator.

Background

The paper derives Dynamic Structural Causal Models (DSCMs) that represent the asymptotic behavior of ordinary differential equations under time-dependent interventions. Although the theoretical construction is established, the resulting structural equations can be complex, even for a simple harmonic oscillator. The paper therefore leaves unresolved the practical problem of deriving data-based parameter-estimation methods, a necessary step toward applications and data-driven causal discovery for oscillatory and more general dynamical systems.

References

Since the DSCM derived for a simple harmonic oscillator (see Example \ref{example:dscm}) is already quite complex, we leave the task of deriving methods that estimate the parameters from data for future work.

— From Deterministic ODEs to Dynamic Structural Causal Models  (1608.08028 - Rubenstein et al., 2016) in Introduction; Section 1, paragraph preceding the roadmap