TITLE: Maximal entropy distribution with given conditionals
QUESTION [7 upvotes]: It is well known that of all the joint distributions $p(x,y)$ with fixed marginals $p(x),p(y)$, the one with the highest entropy is:
$$
p(x,y)=p(x)p(y).
$$
Suppose instead that we have conditionals. Namely:

Which probability distribution $p(x,y,z)$, with fixed $p(x|y)$ and $p(x|z)$, has maximal entropy?

is there even an explicit formula?
(Note: one is tempted to take $p(x,y,z)$ such that $p(x|y,z)=p(x|y)p(x|z)$, but I think this is misleading, right?)
Feel free to edit question and tags appropriately.
Thanks!
(Crossposted from Cross Validated, where nobody could answer.)

REPLY [2 votes]: You can find a full formula in http://arxiv.org/pdf/1512.00752v3.pdf