The causal relationships within them are cyclic, putting them outside the scope of Reichenbach’s principle and Pearl-style causal analysis.
When we start introducing time into the mix I think it can be helpful to be somewhat more particular about how we define variables in a causal setting. When you have limited time resolution measurments of a quantity over time you can view it as a single “variable” that has is involved in a causal cycle. But you could also “unroll” this cycle in time and view the quantity at each time as a seperate variable. If you do this it seems to me like Pearl-style causal analysis generally holds. Even if X and Y have a montonic pattern over time with prior time points of each series causing its later time points but no causal interaction between them, the X(t)s and Y(t)s aren’t correlated with each other, and the pattern over time is fully explained by the causal structure. This makes sense in a Pearl-style analysis because you would have an SCM for the series that looks something like X(t) = f(X(t-1, t-2, ….)), which is treating the X(t)s as seperate variables. The correlation over time of X and Y isn’t a correlation between variables in this model, it involves mixing different variables together. If we treat them seperately it seems like the Pearl-style analysis still works and makes no prediction errors, and in fact has the advantage of being robust to potential interventions.
While (3) gets a mention from time to time, none of the papers I have seen on extending causal analysis to cyclic systems have (IMO) made much progress.
Although I won’t claim to understand all the claims and concepts fully, I’ve found this paper to be interesting and helpful in this regard, and to me some of the concepts seem to have connections to the persective I offer above.
Pearl-style SCMs assume that every single node in a graph is ontologically independent, which makes unrolled models as suggested not particularly great.
From a paper co-authored by Pearl himself:
The problem with using structural causal models is that the language of structural models is simply not expressive enough to capture certain intricate relationships that are important in causal reasoning. The ontological commitment of these models is to facts alone, assignments of values to random variables, much like propositional logic. Just as propositional logic is not a particularly effective tool for reasoning about dynamic situations, it is similarly difficult to express dynamic situations (with objects, relationships, and time) in terms of structural causal models.
I haven’t been active in causality research since about 5 years ago, but I’m not aware of any good solutions to the time problem. I do know there are proposals for models that make improvements for causality involving sets of related variables, e.g.: platelet models. I think our own work on counterfactual probabilistic programming has a pretty strong basis, although the philosophy is fairly abridged in the paper.
When we start introducing time into the mix I think it can be helpful to be somewhat more particular about how we define variables in a causal setting. When you have limited time resolution measurments of a quantity over time you can view it as a single “variable” that has is involved in a causal cycle. But you could also “unroll” this cycle in time and view the quantity at each time as a seperate variable. If you do this it seems to me like Pearl-style causal analysis generally holds. Even if X and Y have a montonic pattern over time with prior time points of each series causing its later time points but no causal interaction between them, the X(t)s and Y(t)s aren’t correlated with each other, and the pattern over time is fully explained by the causal structure. This makes sense in a Pearl-style analysis because you would have an SCM for the series that looks something like X(t) = f(X(t-1, t-2, ….)), which is treating the X(t)s as seperate variables. The correlation over time of X and Y isn’t a correlation between variables in this model, it involves mixing different variables together. If we treat them seperately it seems like the Pearl-style analysis still works and makes no prediction errors, and in fact has the advantage of being robust to potential interventions.
Although I won’t claim to understand all the claims and concepts fully, I’ve found this paper to be interesting and helpful in this regard, and to me some of the concepts seem to have connections to the persective I offer above.
Pearl-style SCMs assume that every single node in a graph is ontologically independent, which makes unrolled models as suggested not particularly great.
From a paper co-authored by Pearl himself:
( https://commonsensereasoning.org/2005/hopkins.pdf )
I haven’t been active in causality research since about 5 years ago, but I’m not aware of any good solutions to the time problem. I do know there are proposals for models that make improvements for causality involving sets of related variables, e.g.: platelet models. I think our own work on counterfactual probabilistic programming has a pretty strong basis, although the philosophy is fairly abridged in the paper.