Multivariate interactions modeling through their manifestations: low dimensional model building via the Cumulant Generating Function

Abstract: Growing dimensionality of data calls for beyond-pairwise interactions quantification. Measures of multidimensional interactions quantification are hindered, among others, by two issues: 1. Interpretation difficulties, 2. the curse of dimensionality. We propose to deal with multidimensional interactions by identifying subject-matter specific "interaction manifestations" and then building a low-dimensional model that reproduces as close as possible such manifestations. We argue that an adequate model building approach is to build the model in the form of a cumulant generating function, i.e. to use joint cumulants as building blocks. The whole approach resembles that of probability inversion in the area of expert knowledge based risk assessment, where a discrimination is made between "elicitation" variables, familiar to the experts, and "target" (or model) variables, consisting of the more abstract parameters of a mathematical model. A synthetic example is provided to illustrate these ideas.