| Abstract: | Graphical models are wildly used to describe conditional dependence relationships among interacting random variables. Among statistical
inference problems of a graphical model, one particular interest is utilizing its
interaction structure to reduce model complexity. As an important approach
to utilizing structural information, decomposition allows a statistical inference
problem to be divided into some sub-problems with lower complexities. In this
paper, to investigate decomposition of covariate-dependent graphical models,
we propose some useful definitions of decomposition of covariate-dependent
graphical models with categorical data in the form of contingency tables. Based
on such a decomposition, a covariate-dependent graphical model can be split
into some sub-models, and the maximum likelihood estimation of this model
can be factorized into the maximum likelihood estimations of the sub-models.
Moreover, some sufficient and necessary conditions of the proposed definitions
of decomposition are studied. |
