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On the toric algebra of graphical models. (English) Zbl 1104.60007
The authors obtain necessary and sufficient conditions for an arbitrary discrete probability distribution to factor according to an undirected graphical model, or a log-linear model, or other more general exponential models. They study decomposable as well as non-decomposable graphical models. Some characterizations of decomposable graphical models are obtained.

MSC:
60E99 Distribution theory
13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
Software:
Macaulay2
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References:
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