Model Representability of Methods for the Analysis of the Dependence Structure of Data

In the spirit of the substantive approach to probabilistic and statistical methods of data analysis, we argue in support of the relevance of what is defined as model representability of data analysis methods. Analyzing the model representability of various algorithms that identify the relationship and dependence structures of data, we show that the algorithm that determines the dependence structure by testing for zero in the inverse covariance matrix corresponds to a poorly interpretable model. A principal-component model is proposed for the analysis of the dependence structure. A number of algorithms and models are described for the analysis of the dependence and relationships structure of data.