A Quotient Space Formulation for Generative Statistical Analysis of Graphical Data

Complex analyses involving multiple, dependent random quantities often lead to graphical models—a set of nodes denoting variables interest, and corresponding edges statistical interactions between nodes. To develop for data, especially towards generative modeling, one needs mathematical representations metrics matching comparing graphs, subsequent tools, such as geodesics, means, covariances. This paper utilizes a quotient structure efficient algorithms computing these quantities, leading useful including principal component analysis, testing, modeling. We demonstrate the efficacy this framework using datasets taken from several problem areas, letters, biochemical structures, social networks.