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paper.bib

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@article{Chalkis:2021,
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author = {Apostolos Chalkis and Vissarion Fisikopoulos},
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title = {{volesti: Volume Approximation and Sampling for Convex
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Polytopes in R}},
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title = {{v}olesti: Volume Approximation and Sampling for Convex
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Polytopes in {R}},
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year = {2021},
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journal = {{The R Journal}},
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doi = {10.32614/RJ-2021-077},
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@article{Chalkis_dingo:2023,
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author = {Apostolos Chalkis and Vissarion Fisikopoulos and Elias Tsigaridas and Haris Zafeiropoulos},
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title = {dingo: a Python package for metabolic flux sampling},
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title = {dingo: a {P}ython package for metabolic flux sampling},
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elocation-id = {2023.06.18.545486},
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year = {2023},
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doi = {10.1101/2023.06.18.545486},
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@article{Chalkis_volume:2023,
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author = {Chalkis, Apostolos and Emiris, Ioannis Z. and Fisikopoulos, Vissarion},
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title = {A Practical Algorithm for Volume Estimation based on Billiard Trajectories and Simulated Annealing},
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title = {A Practical Algorithm for Volume Estimation based on Billiard Trajectories and Simulated Annealing},
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year = {2023},
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issue_date = {December 2023},
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publisher = {Association for Computing Machinery},
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editor = {S. Koyejo and S. Mohamed and A. Agarwal and D. Belgrave and K. Cho and A. Oh},
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pages = {31684--31696},
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publisher = {Curran Associates, Inc.},
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title = {Sampling with Riemannian Hamiltonian Monte Carlo in a Constrained Space},
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title = {Sampling with {R}iemannian {H}amiltonian {M}onte {C}arlo in a Constrained Space},
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url = {https://proceedings.neurips.cc/paper_files/paper/2022/file/cdaa7f07b0c5a7803927d20aa717132e-Paper-Conference.pdf},
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volume = {35},
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year = {2022}
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}
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@article{Chalkis_hmc:2023,
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author = {Chalkis, Apostolos and Fisikopoulos, Vissarion and Papachristou, Marios and Tsigaridas, Elias},
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title = {Truncated Log-concave Sampling for Convex Bodies with Reflective Hamiltonian Monte Carlo},
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title = {Truncated Log-concave Sampling for Convex Bodies with Reflective {H}amiltonian {M}onte {C}arlo},
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year = {2023},
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issue_date = {June 2023},
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publisher = {Association for Computing Machinery},

paper.md

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@@ -56,7 +56,7 @@ The focus of `volesti` is scalability in high dimensions,
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that, depending on the problem at hand, could range from hundreds to thousands of dimensions.
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Another novelty is the ability to handle a variety of different inputs
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for the constrained support of the various distributions.
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`volesti` supports three different types of polyhedra [@Ziegler:1995], spectrahedra [@Ramana:1999]
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`volesti` supports three different types of polyhedra [@Ziegler:1995], spectrahedra [@Ramana:1999],
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and general non-linear convex objects.
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`volesti` relies on `Eigen` library [@eigen] for linear algebra but also supports `MKL` optimizations [@mkl].
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Remarkably, these algorithms, and the corresponding implementations,
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also meet the requirements for high accuracy results
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[@Emiris:2014; @Cousins:2015; @Chalkis_volume:2023; @Kook:2022];
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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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# Acknowledgements
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