Causal inference under feedback

September 17, 2020 — February 19, 2025

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Causality for feedback and continuous fields

There is a fun body of work by what is, in my mind, the Central European causality-ML think tank. There is some high connectivity between various interesting people: Bernhard Schölkopf, Jonas Peters, Joris Mooij, Stephan Bongers, and Dominik Janzing, etc. I would love to understand everything that is going on with their outputs, particularly regarding causality in feedback and control systems.

Punishingly abstract introductions may be found in Bongers et al. (2021) and J. Y. Halpern (2000)/J. Y. Halpern (2000).

I am also curious about their work in causality in continuous fields (Bongers and Mooij 2018; Bongers et al. 2016; Rubenstein et al. 2018).

A feedback loop can destroy correlation: This idea comes up in many places.:

Some people have noted that not only does correlation not imply causality, no correlation also doesn’t imply no causality. Two variables can be causally linked without having an observable correlation. Two examples of people noting this previously are Nick Rowe offering the example of Milton Friedman’s thermostat and Scott Cunningham’s Do Not Confuse Correlation with Causality chapter in Causal Inference: The Mixtape.

We realised that this should be true for any control system or negative feedback loop. As long as the control of a variable is sufficiently effective, that variable won’t be correlated with the variables causally prior to it. We wrote a short blog post exploring this idea if you want to take a closer look. It appears to us that in any sufficiently effective control system, causally linked variables won’t be correlated. This puts some limitations on using correlational techniques to study anything that involves control systems, like the economy, or the human body. The stronger version of this observation, that the only case where causally linked variables aren’t correlated is when they are linked together as part of a control system, may also be true.

Our question for you is, has anyone else made this observation? Is it recognised within statistics? (Maybe this is all implied by Peston’s 1972 “The Correlation between Targets and Instruments”? But that paper seems totally focused on economics and has only 14 citations. And the two examples we give above are both economists.) If not, is it worth trying to give this some kind of formal treatment or taking other steps to bring this to people’s attention, and if so, what would those steps look like?

1 References

Ahsan, Arbour, and Zheleva. 2022. “Relational Causal Models with Cycles: Representation and Reasoning.” In Proceedings of the First Conference on Causal Learning and Reasoning.

Bongers, Forré, Peters, et al. 2021. “Foundations of Structural Causal Models with Cycles and Latent Variables.” The Annals of Statistics.

Bongers, and Mooij. 2018. “From Random Differential Equations to Structural Causal Models: The Stochastic Case.” arXiv:1803.08784 [Cs, Stat].

Bongers, Peters, Schölkopf, et al. 2016. “Structural Causal Models: Cycles, Marginalizations, Exogenous Reparametrizations and Reductions.” arXiv:1611.06221 [Cs, Stat].

Cozman. 2000. “Credal Networks.” Artificial Intelligence.

Getoor, Friedman, Koller, et al. 2001. “Learning Probabilistic Relational Models.” In Relational Data Mining.

Halpern, Joseph Y. 1998. “Axiomatizing Causal Reasoning.” In Proceedings of the Fourteenth Conference on Uncertainty in Artificial Intelligence. UAI’98.

Halpern, J. Y. 2000. “Axiomatizing Causal Reasoning.” Journal of Artificial Intelligence Research.

Lauritzen, and Richardson. 2002. “Chain Graph Models and Their Causal Interpretations.” Journal of the Royal Statistical Society: Series B (Statistical Methodology).

Mooij, Peters, Janzing, et al. 2016. “Distinguishing Cause from Effect Using Observational Data: Methods and Benchmarks.” Journal of Machine Learning Research.

Peters, Janzing, and Schölkopf. 2017. Elements of Causal Inference: Foundations and Learning Algorithms. Adaptive Computation and Machine Learning Series.

Rubenstein, Bongers, Schölkopf, et al. 2018. “From Deterministic ODEs to Dynamic Structural Causal Models.” In Uncertainty in Artificial Intelligence.

Schölkopf. 2022. “Causality for Machine Learning.” In Probabilistic and Causal Inference: The Works of Judea Pearl.

Xu, Tan, Fu, et al. 2022. “Dynamic Causal Collaborative Filtering.” In Proceedings of the 31st ACM International Conference on Information & Knowledge Management. CIKM ’22.