I am trying to construct large joint distributions through smaller joint distributions and I'm not sure how to approach the literature.
I am curious if there exists a function which can take n subjoint distributions and approximate a larger joint distribution.
f(P(X,Y), P(X,Z)) = P(X,Y,Z) + e
I am also curious whether overlapping variables (variables in both sub joint distributions) lower the error in comparison to disjoint sub joint distributions.
P(X,Y,Z,A) - f(P(X,Y,A), P(X,Z)) < P(X,Y,Z,A) - f(P(X,Y), P(Z,A))?
I have a feeling that this has something to do with inclusion-exclusion and mutual information.