Scalable geometric and statistical software

Technologies
python, c++, r, jupyter, github-actions
Topics
mathematics, data science, computational biology, computational geometry, statistics
Scalable geometric and statistical software
GeomScale is a research and development project that delivers open source code for state-of-the-art algorithms for problems at the intersection of data science, optimization, geometric, and statistical computing. The current focus of GeomScale is on 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. 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 python interfaces (the latter is hosted in package dingo), 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. To our knowledge it is the most efficient software package for sampling and volume computation to date. It is, in several cases, orders of magnitude faster compared to packages that solve the same problems. It can be used to compute challenging multivariate integrals and to approximate optimal solutions in optimization problems. It has already found important applications in systems biology by analyzing large metabolic networks (e.g., the latest human network) and in FinTech by detecting shock events and by evaluating portfolios performance in stock markets with thousands of assets. Other application areas include AI and in particular approximate weighted model integration. Recent studies has shown a potential application of volesti methods in trustworthy AI, static analysis of programs and differential privacy.
2022 Program

Successful Projects

Contributor
Zhang Zhuyan
Mentor
Elias Tsigaridas, Marios Papachristou, Cyril
Organization
GeomScale
Automatic differentiation support in volesti
The most efficient algorithm to sample from a log-concave distribution, that volesti supports is the Hamiltonian Monte Carlo with leapfrog...
Contributor
reyan_ahmed
Mentor
Vissarion Fisikopoulos, Apostolos Chalkis, Vangelis Anagnostopoulos
Organization
GeomScale
Counting linear extensions with volume computation
In this project, we will implement different algorithms to count linear extensions approximately. In the problem of counting the linear extensions,...
Contributor
Haris Zafeiropoulos
Mentor
Vissarion Fisikopoulos, Elias Tsigaridas, Apostolos Chalkis
Organization
GeomScale
Memory allocation in facet redundancy removal in dingo
Sampling and volume computation of convex polytopes is a challenging computational problem with many applications in inference from linear...
Contributor
KONSTANTINOS PALLIKARIS
Mentor
Vissarion Fisikopoulos, Apostolos Chalkis, Ioannis Psarros
Organization
GeomScale
Support for new sampling methods and new model formats in dingo
Package dingo is a python package that analyzes metabolic networks. It relies on high dimensional sampling with Markov Chain Monte Carlo (MCMC)...
Contributor
Ioannis Iakovidis
Mentor
Vissarion Fisikopoulos, Elias Tsigaridas, Apostolos Chalkis, Marios Papachristou
Organization
GeomScale
Randomized SDP solver with Riemannian Hamiltonian Monte Carlo
The relationship between sampling and optimization has gained increasing interest in recent years. A great number of optimization algorithms that are...
Contributor
Huu Phuoc Le
Mentor
Elias Tsigaridas, Veniarakelian, echristo
Organization
GeomScale
Sampling correlation matrices
We study the sampling of correlation matrices from a given probability density, which has applications in various scientific, engineering and...