1. Noisy Group Testing (Quick and Efficient) Sheng Cai, Mayank Bakshi, Sidharth Jaggi The Chinese University of Hong Kong Mohammad Jahangoshahi Sharif University of Technology

2. q Group Testing For Pr(error)< ε, Lower bound of number of tests: What’s known [CCJS11] 2 q Chun Lam Chan; Pak Hou Che; Jaggi, S.; Saligrama, V.;, "Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms," 49th Annual Allerton Conference on Communication, Control, and Computing, pp.1832-1839, 28-30 Sept. 2011 [CCJS11] Adaptive vs. Non-adaptive

3. Decoding complexity # Tests  Lower bound Lower bound      Adaptive Non-Adaptive Two-Stage Adaptive This work   O(poly(D)log(N)),O(D 2 log(N)) O(DN),O(Dlog(N)) [NPR12] O(Dlog(N)) 3

4. Hammer: GROTESQUE Testing 4

5. 4

6. 4

7. 4

8. Testing Matrix IN OUT Negative 0 Positive 1 5

9. Multiplicity ? 6

10. Multiplicity (d = 0) 7

11. 7

12. 7

13. 7 d = 0 No positive tests

14. Multiplicity (d = 1) 8

15. 8

16. 8

17. 8 d = 1 50% positive tests

18. Multiplicity (d = 2) 9

19. 9

20. 9

21. 9 d = 2 75% positive tests Statistical Difference!

22. Multiplicity ? 10

23. Localization 11 ?

24. Localization BSC (q) Channel Expander Codes Decoder Signature Test Outcome Particular Signature 12

25. Hammer: GROTESQUE Testing 4

26. Nail: “Good” Partioning N items D defectives 13

27. Adaptive Group Testing Groups 14

28. Adaptive Group Testing 14 Decaying geometrically Tests Groups

29. Adaptive Group Testing 14 The number of unidentified defectives <

30. Adaptive Group Testing 14 Tests of size Coupon Collection

31. Non-Adaptive Group Testing Groupsconstant fraction of “Good” groups Tests 15

32. Non-Adaptive Group Testing 15

33. Non-Adaptive Group Testing 15 Independent partitions Coupon Collection Tests

34. 2-Stage Adaptive Group Testing 16 Groups (Birthdays)

35. 2-Stage Adaptive Group Testing Non-adaptive Group Testing 16 + Tests

36.    Summary of this work Decoding complexity # Tests O(Dlog(N)) 3

37. THANK YOU 謝謝