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Noisy Group T esti ng (quick and efficient )

Noisy Group T esti ng (quick and efficient ). Mohammad Jahangoshahi Sheng Cai Mayank Bakshi Sidharth Jaggi. GROTESQUE : Noisy GRO up TES ting ( QU ick and E fficient). Mohammad Jahangoshahi Sheng Cai Mayank Bakshi Sidharth Jaggi. n-d. q. d. 0. 1. q. 0. 1.

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Noisy Group T esti ng (quick and efficient )

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  1. Noisy Group Testing (quick and efficient) Mohammad Jahangoshahi ShengCai MayankBakshi SidharthJaggi

  2. GROTESQUE: Noisy GROupTESting(QUickand Efficient) Mohammad Jahangoshahi ShengCai MayankBakshi SidharthJaggi

  3. n-d q d 0 1 q 0 1 For Pr(error)< ε , Lower bound: What’s known …[CCJS11] Noisy Combinatorial OMP:

  4. This work #Tests Adaptive  Non-Adaptive  Lower bound Two-Stage Adaptive  [NPR12]  O(poly(D)log(N)),O(D2log(N))  O(DN),O(Dlog(N))    Lower bound Decoding complexity

  5. This work #Tests    Decoding complexity

  6. Hammer: GROTESQUE testing

  7. Multiplicity ?

  8. Localization Noiseless: ? Noisy:

  9. Nail: “Good” Partioning nitems ddefectives GROTESQUE

  10. Adaptive Group Testing • O(n/d)

  11. Adaptive Group Testing GROTESQUE GROTESQUE O(dlog(n)) time, tests, constant fraction recovered GROTESQUE GROTESQUE • O(n/d)

  12. Adaptive Group Testing • Each stage constant fraction recovered • # tests, time decaying geometrically

  13. Adaptive Group Testing • T=O(logD)

  14. Non-Adaptive Group Testing • O(Dlog(D)) • Constant fraction “good”

  15. Non-Adaptive Group Testing • Iterative Decoding

  16. 2-Stage Adaptive Group Testing • =D2

  17. 2-Stage Adaptive Group Testing • =D2 • O(Dlog(D)log(D2)) tests, time

  18. 2-Stage Adaptive Group Testing • =D2 • O(Dlog(D)log(D2)) tests, time • No defectives share the same “birthday” when S=poly(D)

  19. 2-Stage Adaptive Group Testing • =D2 • O(Dlog(N)) tests, time

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