Experimental design is a classical statistics problem, and its aim is to estimate an unknown vector from linear measurements where a Gaussian noise is introduced in each measurement. For the combinatorial experimental design problem, the goal is to pick a subset of experiments so as to make the most accurate estimate of the unknown parameters. In this paper, we will study one of the most robust measures of error estimation—the Doptimality criterion, which corresponds to minimizing the volume of the confidence ellipsoid for the estimation error. The problem gives rise to two natural variants depending on whether repetitions of experimentsmore »
Approximate Positive Correlated Distributions and Approximation Algorithms for Doptimal Design
Experimental design is a classical area in statistics and has also found new applications in machine learning. In the combinatorial experimental design problem, the aim is to estimate an unknown mdimensional vector x from linear measurements where a Gaussian noise is introduced in each measurement. The goal is to pick k out of the given n experiments so as to make the most accurate estimate of the unknown parameter x. Given a set S of chosen
experiments, the most likelihood estimate x0 can be obtained by a least squares computation. One of the robust measures of error estimation is the Doptimality criterion which aims to minimize the generalized variance of the estimator. This corresponds to minimizing the volume of the standard confidence ellipsoid for the estimation error x − x0. The problem gives rise to two natural variants depending on whether repetitions of experiments is allowed or not. The latter variant, while being more general, has also found
applications in geographical location of sensors.
We show a close connection between approximation algorithms for the Doptimal design problem and constructions of approximately mwise positively correlated distributions.
This connection allows us to obtain first approximation algorithms for the Doptimal design problem with and without repetitions. more »
 Award ID(s):
 1717947
 Publication Date:
 NSFPAR ID:
 10065985
 Journal Name:
 Proceedings of the TwentyNinth Annual ACMSIAM Symposium on Discrete Algorithms
 Page Range or eLocationID:
 22402255
 Sponsoring Org:
 National Science Foundation
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