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Maximum-Entropy Sampling

Algorithms and Application

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  • © 2022

Overview

  • Aimed at graduate students and researchers in optimization and data analytics
  • Concerns the MESP at the intersection of optimization algorithms and data science
  • There is no other book on this subject

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About this book

This monograph presents a comprehensive treatment of the maximum-entropy sampling problem (MESP), which is a fascinating topic at the intersection of mathematical optimization and data science. The text situates MESP in information theory, as the algorithmic problem of calculating a sub-vector of pre-specificed size from a multivariate Gaussian random vector, so as to maximize Shannon's differential entropy. The text collects and expands on state-of-the-art algorithms for MESP, and addresses its application in the field of environmental monitoring. While MESP is a central optimization problem in the theory of statistical designs (particularly in the area of spatial monitoring), this book largely focuses on the unique challenges of its algorithmic side. From the perspective of mathematical-optimization methodology, MESP is rather unique (a 0/1 nonlinear program having a nonseparable objective function), and the algorithmic techniques employed are highly non-standard. In particular, successful techniques come from several disparate areas within the field of mathematical optimization; for example: convex optimization and duality, semidefinite programming, Lagrangian relaxation, dynamic programming, approximation algorithms, 0/1 optimization (e.g., branch-and-bound), extended formulation, and many aspects of matrix theory. The book is mainly aimed at graduate students and researchers in mathematical optimization and data analytics.

 

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Keywords

Table of contents (5 chapters)

Authors and Affiliations

  • Department of Systems Engineering and Computer Science, COPPE, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil

    Marcia Fampa

  • Department of Industrial & Operations Engineering, University of Michigan, Ann Arbor, USA

    Jon Lee

Bibliographic Information

  • Book Title: Maximum-Entropy Sampling

  • Book Subtitle: Algorithms and Application

  • Authors: Marcia Fampa, Jon Lee

  • Series Title: Springer Series in Operations Research and Financial Engineering

  • DOI: https://doi.org/10.1007/978-3-031-13078-6

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022

  • Hardcover ISBN: 978-3-031-13077-9Published: 30 October 2022

  • Softcover ISBN: 978-3-031-13080-9Published: 31 October 2023

  • eBook ISBN: 978-3-031-13078-6Published: 29 October 2022

  • Series ISSN: 1431-8598

  • Series E-ISSN: 2197-1773

  • Edition Number: 1

  • Number of Pages: XVII, 195

  • Number of Illustrations: 1 b/w illustrations, 9 illustrations in colour

  • Topics: Optimization, Operations Research, Management Science

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