I’m confused what necessary work the Factorisation is doing in these temporal examples—in your example A and B are independent and C is related to both—the only assignment of “upstream/downstream” relations that makes sense is that C is downstream of both.
Is the idea that factorisation is what carves your massive set of possible worlds up into these variables in the first place? Feel like I’m in a weird position where the math makes sense but I’m missing the motivational intuition for why we want to switch to this framework in the first place
I are note sure what you are asking (indeed I am not sure if you are responding to me or cousin_it.)
One thing that I think is going on is that I use “factorization” in two places. Once when I say Pearl is using factorization data, and once where I say we are inferring a FFS. I think this is a coincidence. “Factorization” is just a really general and useful concept.
So the carving into A and B and C is a factorization of the world into variables, but it is not the kind of factorization that shows up in the FFS, because disjoint factors should be independent in the FFS.
As for why to switch to this framework, the main reason (to me) is that it has many of the advantages of Pearl with also being able to talk about some variables being coarse abstract versions of other variables. This is largely because I am interested in embedded agency applications.
Another reason is that we can’t tell a compelling story about where the variables came from in the Pearlian story. Another reason is that sometimes we can infer time where Pearl cannot.
I’m confused what necessary work the Factorisation is doing in these temporal examples—in your example A and B are independent and C is related to both—the only assignment of “upstream/downstream” relations that makes sense is that C is downstream of both.
Is the idea that factorisation is what carves your massive set of possible worlds up into these variables in the first place? Feel like I’m in a weird position where the math makes sense but I’m missing the motivational intuition for why we want to switch to this framework in the first place
I are note sure what you are asking (indeed I am not sure if you are responding to me or cousin_it.)
One thing that I think is going on is that I use “factorization” in two places. Once when I say Pearl is using factorization data, and once where I say we are inferring a FFS. I think this is a coincidence. “Factorization” is just a really general and useful concept.
So the carving into A and B and C is a factorization of the world into variables, but it is not the kind of factorization that shows up in the FFS, because disjoint factors should be independent in the FFS.
As for why to switch to this framework, the main reason (to me) is that it has many of the advantages of Pearl with also being able to talk about some variables being coarse abstract versions of other variables. This is largely because I am interested in embedded agency applications.
Another reason is that we can’t tell a compelling story about where the variables came from in the Pearlian story. Another reason is that sometimes we can infer time where Pearl cannot.