Scalable algorithms for geometric statistics
GeomScale is a research and development project that delivers open source code for state-of-the-art algorithms at the intersection of data science, optimization, geometric, and statistical computing. The current focus of GeomScale is scalable algorithms for sampling from high-dimensional distributions, integration, convex optimization, and their applications. One of our ambitions is to fill the gap between theory and practice by turning state-of-the-art theoretical tools in geometry and optimization to state-of-the-art implementations. We believe that towards this goal, we will deliver various innovative solutions in a variety of application fields, like finance, computational biology, and statistics that will extend the limits of contemporary computational tools. GeomScale aims in serving as a building block for an international, interdisciplinary, and open community in high dimensional geometrical and statistical computing. The main development is currently performed in volesti, a generic open source C++ library, with R and (limited) Python interfaces, for high-dimensional sampling, volume approximation, and copula estimation for financial modelling.
In particular, the current implementation scales up to hundred or thousand dimensions, depending on the problem. It is the most efficient software package for sampling and volume computation to date with orders of magnitude performance in several cases compared to packages that solves the same problems. It can be used to compute intractable multivariate integrals and to approximate optimal solutions in optimization problems. It has already found important applications in computational economics as, by exploiting approximate volume computation of convex bodies, we use it to detect financial crises and evaluate portfolios performance in large stock markets with hundreds of assets. Other application areas include AI and in particular approximate weighted model integration, and data-driven power systems in control.
GeomScale 2020 Projects
A comparative study of uniform high dimensional samplersUniform sampling from convex polytopes in high dimensions is very useful in many scientific fields and applications. The package volesti is a C++...
Optimization and Sum of SquaresWe aim to provide an implementation of modern approaches to Sum of Squares problems.
Sampling from High-Dimensional log-concave densitiesThis proposal aims to provide functionality on sampling from high-dimensional densities. A log-concave density is a density g(x) proportional to...