# Causal inference in the continuous limit

February 17, 2021 — February 17, 2021

algebra

functional analysis

how do science

machine learning

networks

neural nets

PDEs

probability

sciml

statistics

stochastic processes

Where our causality is over fields of continuously indexed variables rather than discrete nodes, what can we do? Do we talk about light cones? Wave propagation? Covariance?

Unclear.

Graphons look like they should help here, except they do not capture what I would typically imagine about causality, e.g. which covariates influence causation. Something which encodes spatial proximity, or temporal ordering, or other covariates, looks more useful at a glance? Presumably, I am behind the literature.

## 1 References

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*Journal of the Royal Statistical Society: Series A (Statistics in Society)*.
Akbari, Winter, and Tomko. 2023. “Spatial Causality: A Systematic Review on Spatial Causal Inference.”

*Geographical Analysis*.
Blom, Bongers, and Mooij. 2020. “Beyond Structural Causal Models: Causal Constraints Models.” In

*Uncertainty in Artificial Intelligence*.
Bongers, Forré, Peters, et al. 2020. “Foundations of Structural Causal Models with Cycles and Latent Variables.”

*arXiv:1611.06221 [Cs, Stat]*.
Bongers, and Mooij. 2018. “From Random Differential Equations to Structural Causal Models: The Stochastic Case.”

*arXiv:1803.08784 [Cs, Stat]*.
Bronstein. 2022. “Beyond Message Passing: A Physics-Inspired Paradigm for Graph Neural Networks.”

*The Gradient*.
Dash. 2003. “Caveats For Causal Reasoning With Equilibrium Models.”

Dash, and Druzdzel. 2001. “Caveats For Causal Reasoning With Equilibrium Models.” In

*Symbolic and Quantitative Approaches to Reasoning with Uncertainty*.
Glymour. 2007. “When Is a Brain Like the Planet?”

*Philosophy of Science*.
Hansen, and Sokol. 2014. “Causal Interpretation of Stochastic Differential Equations.”

*Electronic Journal of Probability*.
Mogensen, Malinsky, and Hansen. 2018. “Causal Learning for Partially Observed Stochastic Dynamical Systems.” In

*UAI2018*.
Rubenstein, Bongers, Schölkopf, et al. 2018. “From Deterministic ODEs to Dynamic Structural Causal Models.” In

*Uncertainty in Artificial Intelligence*.
Schulam, and Saria. 2017. “Reliable Decision Support Using Counterfactual Models.” In

*Proceedings of the 31st International Conference on Neural Information Processing Systems*. NIPS’17.