摘要
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.
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.
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）.
