I think FFS makes sense as an analog of DAG, and it seems reasonable to think of the normal model as DAG time and this model as FFS time. I think the name made me a bit confused by calling attention to one particular diff between this model and Pearl (factored sets vs variables), whereas I actually feel like that diff was basically a red herring and it would have been fastest to understand if the presentation had gone in the opposite direction by demphasizing that diff (e.g. by presenting the framework with variables instead of factors).
That said, even the DAG/FFS analogy still feels a bit off to me (with the caveat that I may still not have a clear picture / don’t have great aesthetic intuitions about the domain).
Factorization seems analogous to describing a world as a set of variables (and to the extent it’s not analogous it seems like an aesthetic difference about whether to take the world or variables as fundamental, rather than a substantive difference in the formalism) rather than to the DAG that relates the variables.
The structural changes seem more like (i) replacing a DAG with a bipartite graph, (ii) allowing arrows to be deterministic (I don’t know how typically this is done in causal models). And then those structural changes lead to generalizing the usual concepts about causality so that they remain meaningful in this setting.
All that said, I’m terrible at both naming things and presenting ideas, and so don’t want to make much of a bid for changes in either department.
Makes sense. I think a bit of my naming and presentation was biased by being so surprised by the not on OEIS fact.
I think I disagree about the bipartite graph thing. I think it only feels more natural when comparing to Pearl. The talk frames everything in comparison to Pearl, but I think if you are not looking at Pearl, I think graphs don’t feel like the right representation here. Comparing to Pearl is obviously super important, and maybe the first introduction should just be about the path from Pearl to FFS, but once we are working within the FFS ontology, graphs feel not useful. One crux might be about how I am excited for directions that are not temporal inference from statistical data.
My guess is that if I were putting a lot of work into a very long introduction for e.g. the structure learning community, I might start the way you are emphasizing, but then eventually convert to throwing all the graphs away.
(The paper draft I have basically only ever mentions Pearl/graphs for motivation at the beginning and in the applications section.)
I agree that bipartite graphs are only a natural way of thinking about it if you are starting from Pearl. I’m not sure anything in the framework is really properly analogous to the DAG in a causal model.
My thoughts on naming this finite factored sets: I agree with Paul’s observation that
| Factorization seems analogous to describing a world as a set of variables
By calling this ‘finite factored sets’, you are emphasizing the process of coming up with individual random variables, the variables that end up being the (names of the) nodes in a causal graph. With s∈S representing the entire observable 4D history of a world (like a computation starting from a single game of life board state), a factorisation B={b1,b2,⋯bn} splits such s into a tuple of separate, more basic observables (bb1,bb2,⋯,bbn). where bb1∈b1, etc. In the normal narrative that explains Pearl causal graphs, this splitting of the world into smaller observables is not emphasized. Also, the splitting does not necessarily need to be a bijection. It may loose descriptive information with respect to s.
So I see the naming finite factored sets as a way to draw attention to this splitting step, it draws attention to the fact that if you split things differently, you may end up with very different causal graphs. This leaves open the question of course is if really want to name your framework in a way that draws attention to this part of the process. Definitely you spend a lot of time on creating an equivalent to the arrows between the nodes too.
I think FFS makes sense as an analog of DAG, and it seems reasonable to think of the normal model as DAG time and this model as FFS time. I think the name made me a bit confused by calling attention to one particular diff between this model and Pearl (factored sets vs variables), whereas I actually feel like that diff was basically a red herring and it would have been fastest to understand if the presentation had gone in the opposite direction by demphasizing that diff (e.g. by presenting the framework with variables instead of factors).
That said, even the DAG/FFS analogy still feels a bit off to me (with the caveat that I may still not have a clear picture / don’t have great aesthetic intuitions about the domain).
Factorization seems analogous to describing a world as a set of variables (and to the extent it’s not analogous it seems like an aesthetic difference about whether to take the world or variables as fundamental, rather than a substantive difference in the formalism) rather than to the DAG that relates the variables.
The structural changes seem more like (i) replacing a DAG with a bipartite graph, (ii) allowing arrows to be deterministic (I don’t know how typically this is done in causal models). And then those structural changes lead to generalizing the usual concepts about causality so that they remain meaningful in this setting.
All that said, I’m terrible at both naming things and presenting ideas, and so don’t want to make much of a bid for changes in either department.
Makes sense. I think a bit of my naming and presentation was biased by being so surprised by the not on OEIS fact.
I think I disagree about the bipartite graph thing. I think it only feels more natural when comparing to Pearl. The talk frames everything in comparison to Pearl, but I think if you are not looking at Pearl, I think graphs don’t feel like the right representation here. Comparing to Pearl is obviously super important, and maybe the first introduction should just be about the path from Pearl to FFS, but once we are working within the FFS ontology, graphs feel not useful. One crux might be about how I am excited for directions that are not temporal inference from statistical data.
My guess is that if I were putting a lot of work into a very long introduction for e.g. the structure learning community, I might start the way you are emphasizing, but then eventually convert to throwing all the graphs away.
(The paper draft I have basically only ever mentions Pearl/graphs for motivation at the beginning and in the applications section.)
I agree that bipartite graphs are only a natural way of thinking about it if you are starting from Pearl. I’m not sure anything in the framework is really properly analogous to the DAG in a causal model.
My thoughts on naming this finite factored sets: I agree with Paul’s observation that
| Factorization seems analogous to describing a world as a set of variables
By calling this ‘finite factored sets’, you are emphasizing the process of coming up with individual random variables, the variables that end up being the (names of the) nodes in a causal graph. With s∈S representing the entire observable 4D history of a world (like a computation starting from a single game of life board state), a factorisation B={b1,b2,⋯bn} splits such s into a tuple of separate, more basic observables (bb1,bb2,⋯,bbn). where bb1∈b1, etc. In the normal narrative that explains Pearl causal graphs, this splitting of the world into smaller observables is not emphasized. Also, the splitting does not necessarily need to be a bijection. It may loose descriptive information with respect to s.
So I see the naming finite factored sets as a way to draw attention to this splitting step, it draws attention to the fact that if you split things differently, you may end up with very different causal graphs. This leaves open the question of course is if really want to name your framework in a way that draws attention to this part of the process. Definitely you spend a lot of time on creating an equivalent to the arrows between the nodes too.