Contributor
Huu Phuoc Le

Sampling correlation matrices


Mentors
Elias Tsigaridas, Veniarakelian, echristo
Organization
GeomScale
Technologies
c++, r, Spectra, Eigen
Topics
statistics, Random walks, Correlation matrices
We study the sampling of correlation matrices from a given probability density, which has applications in various scientific, engineering and business areas (biology, finances,...). This problem is technically difficult due to the constraints of correlation matrices (entries in [-1,1], positive semi-definiteness). The current methods can only scale to a few tens of dimensions. This project aims to provide efficient C++ implementations for new geometric-flavored algorithms to sample correlation matrices (Arakelian, Chalkis 2021) and integrate them into VolEsti, an open-source high-performance software for sampling, volume computing and geometric statistics. Our main tasks consist of implementing a new class of convex bodies to represent the space of correlation matrices and geometric operations for performing two random walk sampling algorithms (the accelerated billiard walk and Reflective Hamiltonian Monte Carlo algorithm) over those convex bodies. These tasks can be supported by the already existing geometric facilities of VolEsti and the theoretical results found in related works. We will focus mainly on building an optimized C++ code to achieve better scalability for those algorithms and carry out intensive experiment and benchmark with other competitors to justify our efficiency. The expected duration of this project is 175 hours spread over 7 weeks of coding period (June 13 - July 29). The C++ implementation obtained by the end of this project will expand VolEsti towards an all-in-one high-performance statistic tools for research and business uses.