The conditional independence structure of a common probability measure is a structural model. In this paper, we solve an open problem posed by Studeny [Probabilistic Conditional Independence Structures, Theme 9, p. 20...The conditional independence structure of a common probability measure is a structural model. In this paper, we solve an open problem posed by Studeny [Probabilistic Conditional Independence Structures, Theme 9, p. 206]. A new approach is proposed to decompose a directed acyclic graph and its optimal properties are studied. We interpret this approach from the perspective of the decomposition of the corresponding conditional independence model and provide an algorithm for identifying the maximal prime subgraphs in a directed acyclic graph.展开更多
We consider the problems of semi-graphoid inference and of independence implication from a set of conditional-independence statements. Based on ideas from R. Hemmecke et al. [Combin. Probab. Comput., 2008, 17：239 257...We consider the problems of semi-graphoid inference and of independence implication from a set of conditional-independence statements. Based on ideas from R. Hemmecke et al. [Combin. Probab. Comput., 2008, 17：239 257], we present algebraic-geometry characterizations of these two problems, and propose two corresponding algorithms. These algorithms can be realized with any computer algebra system when the number of variables is small.展开更多
文摘The conditional independence structure of a common probability measure is a structural model. In this paper, we solve an open problem posed by Studeny [Probabilistic Conditional Independence Structures, Theme 9, p. 206]. A new approach is proposed to decompose a directed acyclic graph and its optimal properties are studied. We interpret this approach from the perspective of the decomposition of the corresponding conditional independence model and provide an algorithm for identifying the maximal prime subgraphs in a directed acyclic graph.
基金The authors wish to thank the referees for very helpful comments which greatly improved the presentation of this paper. This work was partially supported by the National Natural Science Foundation of China （Grant No. 11025102）, Program for Changjiang Scholars and Innovative Research Team in University, and the Jilin Project （20100401）.
文摘We consider the problems of semi-graphoid inference and of independence implication from a set of conditional-independence statements. Based on ideas from R. Hemmecke et al. [Combin. Probab. Comput., 2008, 17：239 257], we present algebraic-geometry characterizations of these two problems, and propose two corresponding algorithms. These algorithms can be realized with any computer algebra system when the number of variables is small.
