This project originates from a series of papers authored by a group of Japanese researchers in mathematics, data science, and statistics, led by Yuka Hashimoto. In this series, new statistical methods are developed for analysing data based on the theory of operator algebras—particularly so-called Hilbert C*-modules—and it is argued that these methods capture structural features such as continuity and differentiability in certain types of data more effectively than conventional statistical approaches.
The fundamental idea of the project is to combine the theory developed by Hashimoto et al. with the theory of so-called random projections, which allow high-dimensional data to be transformed into a lower-dimensional space where classical statistical methods can be applied computationally efficiently, while largely preserving the essential properties of the original data.
Ultimately, the methods developed in the project will be applied to the analysis of concrete datasets, including studies of twins, in order to investigate the prevention of certain forms of cancer.
This project is made possible by a Project Grant in the Natural and Technical Sciences from the Novo Nordic Foundation and will fund a PhD student.
