1. Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms Chun Lam Chan, Pak Hou Che and Sidharth Jaggi The Chinese University of Hong Kong Venkatesh Saligrama Boston University

2. Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms Chun Lam Chan, Pak Hou Che and Sidharth Jaggi The Chinese University of Hong Kong Venkatesh Saligrama Boston University n-d d

3. Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms Chun Lam Chan, Pak Hou Che and Sidharth Jaggi The Chinese University of Hong Kong Venkatesh Saligrama Boston University n-d d

4. Literature  No error: [DR82], [DRR89]  With small error ϵ :  Upper bound: [AS09], [SJ10] 4

5. Literature  No error: [DR82], [DRR89]  With small error ϵ :  Upper bound: [AS09], [SJ10]  Lower bound: [Folklore] 5

6. Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms

7. Algorithms motivated by Compressive Sensing 7  Combinatorial Basis Pursuit (CBP)  Combinatorial Orthogonal Matching Pursuit (COMP)

8. Noiseless CBP 8 n-d d

9. Noiseless CBP 9 n-d d Discard

10. Noiseless CBP 10  Sample g times to form a group n-d d

11. Noiseless CBP 11  Sample g times to form a group n-d d

12. Noiseless CBP 12  Sample g times to form a group n-d d

13. Noiseless CBP 13  Sample g times to form a group n-d d

14. Noiseless CBP 14  Sample g times to form a group  Total non-defective items drawn: n-d d

15. Noiseless CBP 15  Sample g times to form a group  Total non-defective items drawn:  Coupon collection: n-d d

16. Noiseless CBP 16  Sample g times to form a group  Total non-defective items drawn:  Coupon collection:  Conclusion: n-d d

17. Noisy CBP 17 n-d d

18. Noisy CBP 18 n-d d

19. Noisy CBP 19 n-d d

20. Noisy CBP 20 n-d d

21. Noiseless COMP 21

22. Noiseless COMP 22

23. Noiseless COMP 23

24. Noiseless COMP 24

25. Noiseless COMP 25

26. Noisy COMP 26

27. Noisy COMP 27

28. Noisy COMP 28

29. Noisy COMP 29

30. Noisy COMP 30

31. Noisy COMP 31

32. Noisy COMP 32

33. Simulations 33

34. Simulations 34

35. Summary 35  With small error,

36. End Thanks 36

37. Noiseless COMP x001000100 My 0111000001 0001001001 0100000010 1110001101 0011011001 0000100110 0011011001 37

38. x001000100 My 0111000001 0001001001 0100000010 1110001101 0011011001 0000100110 0011011001 01 01 10x9x9 01 → 0 01 10 01 Noiseless COMP 38

39. Noiseless COMP x001000100 My 0111000001 0001001001 0100000010 1110001101 0011011001 0000100110 0011011001 00 11 00x7x7 11 → 1 11 00 11 39

40. Noiseless COMP x001000100 My 0111000001 0001001001 0100000010 1110001101 0011011001 0000100110 0011011001 11 11 00x4x4 01 → 1 11 00 11 40

41. Noiseless COMP x001000100 My 0111000001 0001001001 0100000010 1110001101 0011011001 0000100110 0011011001 110001 111101 00x4x4 00x7x7 10x9x9 (a)01 → 1(b)11 → 1(c)01 → 0 111101 000010 111101 41

42. Noisy COMP x001000100 My ν ŷ 010100000000 000100100110 010000001011 1110001111+1 → 0 011101000101 000010011000 001101100101 00 00 01 10 11 00 11 42

43. Noisy COMP x001000100 My ν ŷ 010100000000 000100100110 010000001011 1110001111+1 → 0 011101000101 000010011000 001101100101 00 00 01x3x3 10 → 1 11 00 11 43

44. Noisy COMP x001000100 My ν ŷ 010100000000 000100100110 010000001011 1110001111+1 → 0 011101000101 000010011000 001101100101 10 00 11x2x2 10 → 1 11 00 01 44

45. Noisy COMP x001000100 My ν ŷ 010100000000 000100100110 010000001011 1110001111+1 → 0 011101000101 000010011000 001101100101 00 10 01x7x7 10 → 0 01 00 11 45

46. Noisy COMP x001000100 My ν ŷ 010100000000 000100100110 010000001011 1110001111+1 → 0 011101000101 000010011000 001101100101 100000 000010 11x2x2 01x3x3 01x7x7 (a)10 → 1(b)10 → 1(c)10 → 0 111101 000000 011111 46

47. Noisy COMP x001000100 My ν ŷ 010100000000 000100100110 010000001011 1110001111+1 → 0 011101000101 000010011000 001101100101 100000 000010 11x2x2 01x3x3 01x7x7 (a)10 → 1(b)10 → 1(c)10 → 0 111101 000000 011111 47