Improved bounds for noisy group testing with constant tests per item

07/02/2020
by   Oliver Gebhard, et al.
0

The group testing problem is concerned with identifying a small set of infected individuals in a large population. At our disposal is a testing procedure that allows us to test several individuals together. In an idealized setting, a test is positive if and only if at least one infected individual is included and negative otherwise. Significant progress was made in recent years towards understanding the information-theoretic and algorithmic properties in this noiseless setting. In this paper, we consider a noisy variant of group testing where test results are flipped with certain probability, including the realistic scenario where sensitivity and specificity can take arbitrary values. Using a test design where each individual is assigned to a fixed number of tests, we derive explicit algorithmic bounds for two commonly considered inference algorithms and thereby improve on results by Scarlett & Cevher (SODA 2016) and Scarlett & Johnson (2020) and providing the strongest performance guarantees currently proved for efficient algorithms in these noisy group testing models.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset