-

 

 

 




Optimization Online





 

Approximate Positively Correlated Distributions and Approximation Algorithms for D-optimal Design

Mohit Singh (mohitsinghr***at***gmail.com)
Weijun Xie (wxie***at***vt.edu)

Abstract: Experimental design is a classical problem in statistics and has also found new applications in machine learning. In the experimental design problem, the aim is to estimate an unknown vector x in m-dimensions 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 x' can be obtained by a least squares computation. One of the robust measures of error estimation is the D-optimality 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-x'. The problem gives rise to two natural variants depending on whether repetitions are allowed or not. The latter variant, while being more general, has also found applications in the geographical location of sensors. In this work, we first show that a 1/e-approximation for the D-optimal design problem with and without repetitions giving us the first constant factor approximation for the problem. We also consider the case when the number of experiments chosen is much larger than the dimension of the measurements and provide an asymptotically optimal approximation algorithm.

Keywords: Approximation Algorithms, D-Optimal Design, Statistics, Convex Relaxation

Category 1: Combinatorial Optimization (Approximation Algorithms )

Category 2: Applications -- Science and Engineering (Data-Mining )

Citation: working paper

Download: [PDF]

Entry Submitted: 12/08/2017
Entry Accepted: 12/31/2018
Entry Last Modified: 01/15/2018

Modify/Update this entry


  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository

 

Submit
Update
Policies
Coordinator's Board
Classification Scheme
Credits
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Optimization Society