I followed approximately the technical discussion, and now I’m wondering what that would buy us if you are correct.
Max entropy distributions seem nicely behaved and well-studied, so maybe we get some computations, properties, derivation for free? (Basically applying a productive frame to the problem of abstraction)
It would reduce computing the influence of the summary statistics on the model to computing the constraints, as I’m guessing that this is the hard part in computing the max entropy distribution (?)
That’s basically correct; the main immediate gain is that it makes it much easier to compute abstractions and compute using abstractions.
One additional piece is that it hints towards a probably-more-fundamental derivation of the theorems in which maximum entropy plays a more central role. The maximum entropy Telephone Theorem already does that, but the resampling + gKPD approach routes awkwardly through gKPD instead; there’s probably a nice way to do it directly via constrained maximization of entropy. That, in turn, would probably yield stronger and simpler theorems.
I followed approximately the technical discussion, and now I’m wondering what that would buy us if you are correct.
Max entropy distributions seem nicely behaved and well-studied, so maybe we get some computations, properties, derivation for free? (Basically applying a productive frame to the problem of abstraction)
It would reduce computing the influence of the summary statistics on the model to computing the constraints, as I’m guessing that this is the hard part in computing the max entropy distribution (?)
Are these correct, and what am I missing?
That’s basically correct; the main immediate gain is that it makes it much easier to compute abstractions and compute using abstractions.
One additional piece is that it hints towards a probably-more-fundamental derivation of the theorems in which maximum entropy plays a more central role. The maximum entropy Telephone Theorem already does that, but the resampling + gKPD approach routes awkwardly through gKPD instead; there’s probably a nice way to do it directly via constrained maximization of entropy. That, in turn, would probably yield stronger and simpler theorems.