Dependence Structure Estimation via Copula

We propose a new framework for dependence structure learning via copula. Copula is a statistical theory on dependence and measurement of association. Graphical models are considered as a type of special case of copula families, named product copula. In this paper, a nonparametric algorithm for copula estimation is presented. Then a Chow-Liu like method based on dependence measure via copula is proposed to estimate maximum spanning product copula with only bivariate dependence relations. The advantage of the framework is that learning with empirical copula focuses only on dependence relations among random variables, without knowing the properties of individual variables. Another advantage is that copula is a universal model of dependence and therefore the framework based on it can be generalized to deal with a wide range of complex dependence relations. Experiments on both simulated data and real application data show the effectiveness of the proposed method.