... Proceedings of the 47th Annual Meeting of the ACL and the 4th IJCNLP of the AFNLP, pages 360–368,Suntec, Singapore, 2-7 August 2009.c2009 ACL and AFNLPSemi-supervised Learning of Dependency ... x.By relating the sum of the scores of all possibletrees to counting the number of spanning trees in agraph, it can be shown that Zxis the determinant of the Kirchoff matrix K, which is ... marginalprobability of a particular edge k → i (i.e. yi=k),the score of any edge k→ i such that k= k isset to 0. The determinant of the resulting modi-fied Kirchoff matrix Kk→iis then the sum of...