A comparative study of uniform high dimensional samplers  GeomScale/gsoc2020 GitHub Wiki
Overview
Sampling from the uniform distribution of a convex region is a well studied problem useful in many applications and lies in the core of GeomScale activities. This project aims (a) to implement the random walks for uniform sampling that are not implemented in volesti
, (b) to implement the most important statistical tests for checking convergence to the target distribution, (c) to compare the mixing times in practice through extensive experiments.
Related work
Details of your coding project
 New algorithms for uniform sampling
 Comparison with existing ones / Implement statistical tests for convergence
 Polytope database for evaluation of the methods
 Documentation / R vignette
Expected impact
The projects aims in creating a reference point in practical sampling from convex regions in highdimensions (upto order of thousands).
Mentors

Apostolos Chalkis <tolis.chal at gmail.com> is a PhD student in Computer Science. His research focuses on mathematical computing, optimization and computational finance. He has previous experience in GSoC 2018 and 2019 as a student under Org.
Rproject
, implementing stateoftheart algorithms for sampling from high dimensional multivariate distributions. He is one of the authors ofvolesti
. 
Vissarion Fisikopoulos <vissarion.fisikopoulos at gmail.com> is an international expert in mathematical software, computational geometry and optimization, and has previous GSOC mentoring experience with Boost C++ libraries (20162017) and the Rproject (2017).

Elias Tsigaridas <elias.tsigaridas at inria.fr> is an expert in computational nonlinear algebra and geometry with experience in mathematical software. He has contributed to the implementation, in C and C++, of several solving algorithms for various open source computer algebra libraries and has previous GSOC mentoring experience with the Rproject (2019).
Students, please contact all mentors after completing at least one of the tests below.
Tests
Students, please do one or more of the following tests before contacting the mentors above.
 Easy: compile and run VolEsti. Use the R extension to visualize sampling in a polytope.
 Medium: Sample approximate uniformly points from a 100dimensional hypercube using the implmented in
volesti
random walks, for various walk lengths. For each sample project the points to the plane and comment on the mixing of the random walks.  Hard: Use a simple statistical test for convergence of a random walk sampler. Check the convergence of the implemented in
volesti
random walks for a 100dimensional hypercube.
Solutions of tests
Students, please post a link to your test results here.
 EXAMPLE STUDENT 1 NAME, LINK TO GITHUB PROFILE, LINK TO TEST RESULTS.