Formal Analysis of Statistical Dependence Based Homological Algebra - Tsumoto, Shusaku; Hirano, Shoji (2014 IEEE/WIC/ACM International Joint Conferences on Web Intelligence (WI) and Intelligent Agent Technologies (IAT), 2014)
This paper proposes homological analysis of statistical dependency graph. If a dependency graph model satisfy the condition of a chain complex, homological algebra can be applied. Especially, the degree of freedom can be viewed as a dual space of an original complex.