The reason why we usually wouldn’t have found this causal direction using causal graphs is that we wouldn’t even have considered Z as potentially interesting. This is what factored sets give us: They make us consider every possible way of defining variables, so we don’t miss out on any information that may be hidden if we just look at a predetermined set of variables.
I don’t quite understand how this conclusion is reached. Referring to the previous section:
Yes—here is a model that actually works for P:
What is the procedure by which we identify the particular set factorization that models our distribution? Is this identification in some meaningful sense easier than guessing Z directly? I’m just confused about what has been gained here.
What is the procedure by which we identify the particular set factorization that models our distribution?
There is not just one factored set which models the distribution, but infinitely many. The depicted model is just a prototypical example.
The procedure for finding causal relationships (e.g.X→Y in our case) is not trivial. In that part of his post, Scott sounds like it’s
1. have the suspicion that X→Y 2. prove it using the histories
I think there is probably a formalized procedure to find causal relationships using factored sets, but I’m not sure if it’s written up somewhere.
For causal graphs, I don’t know if there is a formalized procedure to find causal relationships which take into account all possible ways to define variables on the sample space. My general impression is that causal graphs become pretty unwieldy once we introduce deterministic nodes. And then many rules we usually use with causal graphs don’t hold anymore, and working with graphs then becomes really unintuitive.
So my intuition is that yes, finding causal relationships while taking into account all possible ways to define variables is easier with factored sets than with causal graphs. (And I’m not even sure if it’s even possible in general with causal graphs.) But my intuition on this isn’t based on knowing a formal procedure for finding causal relationships, it just comes from my impression when playing around with the two different representations.
I don’t quite understand how this conclusion is reached. Referring to the previous section:
What is the procedure by which we identify the particular set factorization that models our distribution? Is this identification in some meaningful sense easier than guessing Z directly? I’m just confused about what has been gained here.
There is not just one factored set which models the distribution, but infinitely many. The depicted model is just a prototypical example.
The procedure for finding causal relationships (e.g.X→Y in our case) is not trivial. In that part of his post, Scott sounds like it’s
1. have the suspicion that X→Y
2. prove it using the histories
I think there is probably a formalized procedure to find causal relationships using factored sets, but I’m not sure if it’s written up somewhere.
For causal graphs, I don’t know if there is a formalized procedure to find causal relationships which take into account all possible ways to define variables on the sample space. My general impression is that causal graphs become pretty unwieldy once we introduce deterministic nodes. And then many rules we usually use with causal graphs don’t hold anymore, and working with graphs then becomes really unintuitive.
So my intuition is that yes, finding causal relationships while taking into account all possible ways to define variables is easier with factored sets than with causal graphs. (And I’m not even sure if it’s even possible in general with causal graphs.) But my intuition on this isn’t based on knowing a formal procedure for finding causal relationships, it just comes from my impression when playing around with the two different representations.