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An Exact Algorithm for Maximum Entropy Sampling

Author

Listed:
  • Chun-Wa Ko

    (Rutgers University, New Brunswick, New Jersey)

  • Jon Lee

    (University of Kentucky, Lexington, Kentucky)

  • Maurice Queyranne

    (University of British Columbia, Vancouver, British Columbia, Canada)

Abstract

We study the experimental design problem of selecting a most informative subset, having prespecified size, from a set of correlated random variables. The problem arises in many applied domains, such as meteorology, environmental statistics, and statistical geology. In these applications, observations can be collected at different locations, and possibly, at different times. Information is measured by “entropy.” In the Gaussian case, the problem is recast as that of maximizing the determinant of the covariance matrix of the chosen subset. We demonstrate that this problem is NP-hard. We establish an upper bound for the entropy, based on the eigenvalue interlacing property, and we incorporate this bound in a branch-and-bound algorithm for the exact solution of the problem. We present computational results for estimated covariance matrices that correspond to sets of environmental monitoring stations in the United States.

Suggested Citation

  • Chun-Wa Ko & Jon Lee & Maurice Queyranne, 1995. "An Exact Algorithm for Maximum Entropy Sampling," Operations Research, INFORMS, vol. 43(4), pages 684-691, August.
    • Handle: RePEc:inm:oropre:v:43:y:1995:i:4:p:684-691
    DOI: 10.1287/opre.43.4.684
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    Citations

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    Cited by:

    1. Hessa Al-Thani & Jon Lee, 2020. "An R Package for Generating Covariance Matrices for Maximum-Entropy Sampling from Precipitation Chemistry Data," SN Operations Research Forum, Springer, vol. 1(3), pages 1-21, September.
    2. Theodore T. Allen & Olivia K. Hernand & Abdullah Alomair, 2020. "Optimal Off-line Experimentation for Games," Decision Analysis, INFORMS, vol. 17(4), pages 277-298, December.
    3. Kurt M. Anstreicher, 2018. "Maximum-entropy sampling and the Boolean quadric polytope," Journal of Global Optimization, Springer, vol. 72(4), pages 603-618, December.
    4. Linda Altieri & Daniela Cocchi, 2021. "Spatial Sampling for Non‐compact Patterns," International Statistical Review, International Statistical Institute, vol. 89(3), pages 532-549, December.
    5. Zhongzhu Chen & Marcia Fampa & Jon Lee, 2023. "On Computing with Some Convex Relaxations for the Maximum-Entropy Sampling Problem," INFORMS Journal on Computing, INFORMS, vol. 35(2), pages 368-385, March.
    6. Boyang Shang & Daniel W. Apley & Sanjay Mehrotra, 2023. "Diversity Subsampling: Custom Subsamples from Large Data Sets," INFORMS Joural on Data Science, INFORMS, vol. 2(2), pages 161-182, October.
    7. HOFFMAN, Alan & LEE, Jon & WILLIAMS, Joy, 2000. "New upper bounds for maximum-entropy sampling," LIDAM Discussion Papers CORE 2000012, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Goldengorin, Boris, 2009. "Maximization of submodular functions: Theory and enumeration algorithms," European Journal of Operational Research, Elsevier, vol. 198(1), pages 102-112, October.
    9. repec:dgr:rugsom:99a17 is not listed on IDEAS
    10. Boris Goldengorin & Gerard Sierksma & Gert A. Tijssen & Michael Tso, 1999. "The Data-Correcting Algorithm for the Minimization of Supermodular Functions," Management Science, INFORMS, vol. 45(11), pages 1539-1551, November.
    11. Kurt M. Anstreicher, 2020. "Efficient Solution of Maximum-Entropy Sampling Problems," Operations Research, INFORMS, vol. 68(6), pages 1826-1835, November.
    12. Goldengorin, Boris & Tijssen, Gert A. & Tso, Michael, 1999. "The maximization of submodular functions : old and new proofs for the correctness of the dichotomy algorithm," Research Report 99A17, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    13. Yildiz, Anil & Mern, John & Kochenderfer, Mykel J. & Howland, Michael F., 2023. "Towards sequential sensor placements on a wind farm to maximize lifetime energy and profit," Renewable Energy, Elsevier, vol. 216(C).

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