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Convex Relaxation for the Generalized Maximum-Entropy Sampling Problem

Authors Gabriel Ponte , Marcia Fampa , Jon Lee

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Author Details

Gabriel Ponte
  • University of Michigan, Ann Arbor, MI, USA
Marcia Fampa
  • Universidade Federal do Rio de Janeiro, Brazil
Jon Lee
  • University of Michigan, Ann Arbor, MI, USA

Funding

  • Ponte, Gabriel: Supported in part by CNPq GM-GD scholarship 161501/2022-2.
  • Fampa, Marcia: Supported in part by CNPq grant 307167/2022-4.
  • Lee, Jon: Supported in part by AFOSR grant FA9550-22-1-0172.

Cite As Get BibTex

Gabriel Ponte, Marcia Fampa, and Jon Lee. Convex Relaxation for the Generalized Maximum-Entropy Sampling Problem. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 25:1-25:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.SEA.2024.25

Abstract

The generalized maximum-entropy sampling problem (GMESP) is to select an order-s principal submatrix from an order-n covariance matrix, to maximize the product of its t greatest eigenvalues, 0 < t ≤ s < n. It is a problem that specializes to two fundamental problems in statistical design theory: (i) maximum-entropy sampling problem (MESP); (ii) binary D-optimality (D-Opt). In the general case, it is motivated by a selection problem in the context of PCA (principal component analysis).
We introduce the first convex-optimization based relaxation for GMESP, study its behavior, compare it to an earlier spectral bound, and demonstrate its use in a branch-and-bound scheme. We find that such an approach is practical when s-t is very small.

Subject Classification

ACM Subject Classification
  • Theory of computation → Mixed discrete-continuous optimization
  • Mathematics of computing → Mathematical optimization
Keywords
  • maximum-entropy sampling
  • D-optimality
  • convex relaxation
  • branch-and-bound
  • integer nonlinear optimization
  • principal component analysis

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References

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