volesti: Volume Approximation and Sampling for Convex Polytopes in R
Apostolos Chalkis, Vissarion Fisikopoulos
Abstract
Sampling from high-dimensional distributions and volume approximation of convex bodies are fundamental operations that appear in optimization, finance, engineering, artificial intelligence, and machine learning. In this paper, we present volesti, an R package that provides efficient, scalable algorithms for volume estimation, uniform, and Gaussian sampling from convex polytopes. volesti scales to hundreds of dimensions, handles efficiently three different types of polyhedra and provides non existing sampling routines to R. We demonstrate the power of volesti by solving several challenging problems using the R language.
Topics & Concepts
PolytopePolyhedronVolume (thermodynamics)Sampling (signal processing)Regular polygonConvex polytopeGaussianComputer scienceScalabilityMixed volumeMathematical optimizationMathematicsAlgorithmConvex optimizationDiscrete mathematicsCombinatoricsConvex setGeometryPhysicsComputer visionDatabaseFilter (signal processing)Quantum mechanicsMarkov Chains and Monte Carlo MethodsBayesian Methods and Mixture ModelsGenerative Adversarial Networks and Image Synthesis