Maximum-Entropy Sampling:
Algorithms and Application
Authors: Marcia Fampa, Jon Lee
Part of the book series: Springer Series in Operations Research and
Financial Engineering (ORFE)
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.
Published: 30 October 2022
https://doi.org/10.1007/978-3-031-13078-6
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