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Recent Advances in Maximum-Entropy Sampling

Marcia Fampa, Jon Lee

TL;DR

In 2022, the book Maximum-Entropy Sampling: Algorithms and Application: Algorithms and Application (Springer) was published and several notable advancements on this topic were surveyed.

Abstract

In 2022, we published the book Maximum-Entropy Sampling: Algorithms and Application (Springer). Since then, there have been several notable advancements on this topic. In this manuscript, we survey some recent highlights.

Recent Advances in Maximum-Entropy Sampling

TL;DR

In 2022, the book Maximum-Entropy Sampling: Algorithms and Application: Algorithms and Application (Springer) was published and several notable advancements on this topic were surveyed.

Abstract

In 2022, we published the book Maximum-Entropy Sampling: Algorithms and Application (Springer). Since then, there have been several notable advancements on this topic. In this manuscript, we survey some recent highlights.

Paper Structure

This paper contains 20 sections, 13 theorems, 51 equations.

Table of Contents

  1. Complexity
  2. Solvable cases
  3. Hardness
  4. Computing
  5. General purpose solvers
  6. Alternating Directions Methods of Multipliers
  7. ADMM for the linx bound
  8. ADMM for the factorization bound
  9. ADMM for the BQP bound
  10. Bound-improvement techniques
  11. Masking
  12. Generalized scaling
  13. Generalized scaling for the BQP bound
  14. Generalized scaling for the linx bound
  15. Generalized scaling for the factorization bound
  16. ...and 5 more sections

Key Result

Lemma 1

Let $\lambda\in\mathbb{R}_+^k$ satisfy $\lambda_1\geq \lambda_2\geq \cdots\geq \lambda_k$ , define $\lambda_0:=+\infty$, and let $s$ be an integer satisfying $0<s\leq k$. Then there exists a unique integer $i$, with $0\leq i< s$, such that

Theorems & Definitions (20)

  • Lemma 1: Nikolov
  • Theorem 2: ALTHANI2023120
  • proof
  • Theorem 3: ALTHANI2023120
  • Theorem 4: ChenFampaLeeGenScaling
  • Theorem 5: ChenFampaLeeGenScaling
  • Theorem 6: see ChenFampaLeeGenScaling for a more detailed statement
  • Theorem 7: li2022d
  • proof
  • Theorem 8: li2022d
  • ...and 10 more