A Quotient Space Formulation for Generative Statistical Analysis of Graphical Data

Understand

Complex analyses involving multiple, dependent random quantities often lead to graphical models - a set of nodes denoting variables of interest, and corresponding edges denoting statistical interactions between nodes.

• To develop statistical analyses for graphical data, especially towards generative modeling, one needs mathematical representations and metrics for matching and comparing graphs, and subsequent tools, such as geodesics, means, and covariances.
• This paper utilizes a quotient structure to develop efficient algorithms for computing these quantities, leading to useful statistical tools, including principal component analysis, statistical testing, and modeling.
• We demonstrate the efficacy of this framework using datasets taken from several problem areas, including letters, biochemical structures, and social networks.