Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Notation
- Part One Machine Learning
- Part Two Optimal Recovery
- Part Three Compressive Sensing
- Executive Summary
- 14 Sparse Recovery from Linear Observations
- 15 The Complexity of Sparse Recovery
- 16 Low-Rank Recovery from Linear Observations
- 17 Sparse Recovery from One-Bit Observations
- 18 Group Testing
- Part Four Optimization
- Part Five Neural Networks
- Appendices
- References
- Index
18 - Group Testing
from Part Three - Compressive Sensing
Published online by Cambridge University Press: 21 April 2022
Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Notation
- Part One Machine Learning
- Part Two Optimal Recovery
- Part Three Compressive Sensing
- Executive Summary
- 14 Sparse Recovery from Linear Observations
- 15 The Complexity of Sparse Recovery
- 16 Low-Rank Recovery from Linear Observations
- 17 Sparse Recovery from One-Bit Observations
- 18 Group Testing
- Part Four Optimization
- Part Five Neural Networks
- Appendices
- References
- Index
Summary
A Boolean analog of the standard compressive sensing problem, known as nonadaptive group testing, is analyzed in this chapter. Its success is characterized via the notion of separability (intimately related to disjunctiveness and strong selectivity) of the testing procedure. The minimal number of tests making separability possible is determined, and a deterministic procedure using roughly this number of tests is presented. Finally, it is shown that solving a linear feasibility program allows one to exactly recover sparse binary vectors from the outcomes of a separable testing procedure.
- Type
- Chapter
- Information
- Mathematical Pictures at a Data Science Exhibition , pp. 149 - 156Publisher: Cambridge University PressPrint publication year: 2022