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however several existing published methods are available as part of propertiary packages (MATLAB) [@Cousins:2015; @Kook:2022].
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however several existing published methods are only available as part of propertiary packages (MATLAB) [@Cousins:2015; @Kook:2022].
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Our open-source package -- `volesti` -- offers all of the aforementioned functionality, together with the support of sampling from general log-concave densities [@Chalkis_hmc:2023], and uniform sampling from spectrahedra [@Chalkis_spectra:2022].
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Our implementation:
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1. supports various sampling techniques based on geometric walks; roughly speaking these are a continuous version of MCMC algorithms, such as Billard walk, Hamiltonian walk and others,
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2. gives the user the ability to sample from various distributions, like uniform, exponential, Gaussian, and general log-concave densities,
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3. allows to consider the distributions constrained in various convex domains, such as hypercubes, zonotopes, general polytopes (defined either as a set of linear inequalities or as a convex hull of a pointset), spectrahedra (feasible sets of semidefinite programs), and,
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3. allows to consider the distributions constrained in various convex domains, such as hypercubes, zonotopes, general polytopes (defined either as a set of linear inequalities or as a convex hull of a pointset), spectrahedra (feasible sets of semidefinite programs), and
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4. can perform volume computations, integration, and solve problems from real life applications in very high dimensions.
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# Impact
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`volesti` has been used extensively in various research and engineering projects coauthored by the authors of this paper.
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In particular, for the problem of sampling the flux space of metabolic networks
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we were able to sample from the most complicated human metabolic network accessible today, Recon3D [@cftz-socg021],
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used to model financial crises [@ccef-crises-j],
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to model financial crises [@ccef-crises-j],
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to detect low volatility anomalies in stock markets [@bcft-aistats-23],
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to introduce randomized control in asset pricing and portfolio performance evaluation [@bcft-arxiv-24]), but also to sample from (and compute the volume of) spectrahedra [@Chalkis_spectra:2022], the feasible regions of semidefinite programs.
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to introduce randomized control in asset pricing and portfolio performance evaluation [@bcft-arxiv-24]), and also to sample from (and compute the volume of) spectrahedra [@Chalkis_spectra:2022], the feasible regions of semidefinite programs.
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Even more, `volesti` has been used by other research teams in conducting research in electric power systems [@Venzke:2019], for problems in probabilistic inference [@Spallitta:2024],
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`volesti` has also been used by other research teams in conducting research in electric power systems [@Venzke:2019], for problems in probabilistic inference [@Spallitta:2024],
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to perform resource analysis on programs [@pham-phd-2024];
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but also for more theoretical and mathematical challenges, like the computation of topological invariants [@co-alenex-2021], and persistent homology [@vm-fods-2022].
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and also for more theoretical and mathematical challenges, like the computation of topological invariants [@co-alenex-2021] and persistent homology [@vm-fods-2022].
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