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无环有向混合图的嵌套马尔可夫性质AI 解读

Conditional independence models associated with directed acyclic graphs (DAGs) may be characterized in at least three different ways: via a factorization, the global Markov property (given by the d-separation criterion), and the local Markov property. Marginals of DAG models also imply equality constraints that are not conditional independences; the well-known “Verma constraint” is an example. Constraints of this type are used for testing edges, and in a computationally…

模型选择与局部几何AI 解读

We consider problems in model selection caused by the geometry of models close to their points of intersection. In some cases—including common classes of causal or graphical models, as well as time series models—distinct models may nevertheless have identical tangent spaces. This has two immediate consequences: first, in order to obtain constant power to reject one model in favour of another we need local alternative hypotheses that decrease to the null at a slower rate than…

离散数据的马尔可夫无环有向混合图AI 解读

Acyclic directed mixed graphs (ADMGs) are graphs that contain directed ($\rightarrow$) and bidirected ($\leftrightarrow$) edges, subject to the constraint that there are no cycles of directed edges. Such graphs may be used to represent the conditional independence structure induced by a DAG model containing hidden variables on its observed margin. The Markovian model associated with an ADMG is simply the set of distributions obeying the global Markov property, given via a…

图形马尔可夫模型的边际对数线性参数AI 解读

Summary Marginal log-linear (MLL) models provide a flexible approach to multivariate discrete data. MLL parameterizations under linear constraints induce a wide variety of models, including models that are defined by conditional independences. We introduce a subclass of MLL models which correspond to acyclic directed mixed graphs under the usual global Markov property. We characterize for precisely which graphs the resulting parameterization is variation independent. The MLL…