On the toric algebra of graphical models
给出了离散概率分布可分解为无向图模型或对数线性模型的充要条件，发现非可分解图模型的条件独立性条件不成立且极大似然估计可能非有理数，并据此提出了可分解图模型的若干新刻画。
We formulate 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. For decomposable graphical models these conditions are equivalent to a set of conditional independence statements similar to the Hammersley–Clifford theorem; however, we show that for nondecomposable graphical models they are not. We also show that nondecomposable models can have nonrational maximum likelihood estimates. These results are used to give several novel characterizations of decomposable graphical models.