Maximum-Entropy Sampling

Algorithms and Application

Marcia Fampa, Jon Lee

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English

Springer International Publishing AG
31 October 2023

Operational research; Optimisation

Series: Springer Series in Operations Research and Financial Engineering

Summary
Details

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.

By: Marcia Fampa, Jon Lee
Imprint: Springer International Publishing AG
Country of Publication: Switzerland
Edition: 2022 ed.
Dimensions: Height: 235mm, Width: 155mm,
Weight: 338g
ISBN: 9783031130809
ISBN 10: 3031130804
Series: Springer Series in Operations Research and Financial Engineering
Pages: 195
Publication Date: 31 October 2023
Audience: College/higher education , Further / Higher Education
Format: Paperback
Publisher's Status: Active