There is an unknown joint multivariate distribution P(A_1, A_2, A_3, ..., A_n) (in my scenario, it's a n-dimensional contingency table), which we need to sample from.
Given an arbitrary set of marginal distributions, e.g., {P(A, B), P(A, C), P(B, C)} from an unknown P(A, B, C), or {P(A, B), P(B, C, D), P(A, D)} from a P(A, B, C, D), how could we generate a set of samples converge to all these given marginal distributions?
Iterative proportional fitting is unfeasible since it involves 2^n - 1 calculation (the number of cells in contingency table) per iteration. And the number of samples needed is much less than the number of cells.
I've checked Loglinear model and Chow-Liu tree, but have no idea. They are used when building an approximation of a given contingency table.
Thanks in advance!