Model Invariants in Algebraic Statistics

The goal of this research project is to develop new methods for data analysis based on algebraic statistics, demonstrate their effectiveness on real data problems, and make them available to the public as software packages.Three algebraic model invariants are central to this action: the maximum likelihood (ML) degree, the Euclidean distance (ED) degree, and the polar degree.

Recently developed in theoretical research, these invariants promise to unlock new algebraic methods for data analysis.

This action will realize this vision, expand the underlying theoretical foundations as needed, and produce statistical tools fit for use by practitioners.The expected impact of this research is fourfold.

First, the obtained results will ground the latest theoretical advances in real applications, improving the algebraic statistics community's sense of what is possible and directing future research. Second, they will generate new mathematically interesting results tailored to the data applications of the project.

Third, they will produce novel insights about complicated data problems with an algebraic structure, strengthening the case for algebra and geometry in data analysis.

Fourth, the easily accessible software produced during this action will introduce algebraic techniques to the data analysis toolkits of data practitioners and domain experts.