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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!

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  • $\begingroup$ Could you be a bit more specific? In general, the marginal distributions are not enough to recover the entire distribution. $\endgroup$
    – Arthur B
    Apr 2, 2012 at 15:02
  • $\begingroup$ The only restriction is the set of marginals. I need ONE among those joint distributions which satisfy the given set of marginals. Since the final purpose is to sample from such a distribution, there is, maybe, no need to fully construct the joint distribution $\endgroup$
    – Jun Zhang
    Apr 2, 2012 at 16:06
  • $\begingroup$ You're able to sample from the full distribution iff you can reconstruct the full distribution. $\endgroup$
    – Arthur B
    Apr 2, 2012 at 19:46

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