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Chun Lam Chan , Pak Hou Che and Sidharth Jaggi The Chinese University of Hong Kong

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

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Chun Lam Chan , Pak Hou Che and Sidharth Jaggi The Chinese University of Hong Kong

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  1. Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms VenkateshSaligrama Boston University Chun Lam Chan, Pak HouChe and SidharthJaggi The Chinese University of Hong Kong

  2. n-d d Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms VenkateshSaligrama Boston University Chun Lam Chan, Pak HouChe and SidharthJaggi The Chinese University of Hong Kong

  3. n-d d Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms VenkateshSaligrama Boston University Chun Lam Chan, Pak HouChe and SidharthJaggi The Chinese University of Hong Kong

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

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

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

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

  8. n-d Noiseless CBP d

  9. n-d Noiseless CBP d Discard

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

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

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

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

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

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

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

  17. n-d Noisy CBP d

  18. n-d Noisy CBP d

  19. n-d Noisy CBP d

  20. n-d Noisy CBP d

  21. Noiseless COMP

  22. Noiseless COMP

  23. Noiseless COMP

  24. Noiseless COMP

  25. Noiseless COMP

  26. Noisy COMP

  27. Noisy COMP

  28. Noisy COMP

  29. Noisy COMP

  30. Noisy COMP

  31. Noisy COMP

  32. Noisy COMP

  33. Simulations

  34. Simulations

  35. Summary • With small error ,

  36. End Thanks

  37. Noiseless COMP

  38. Noiseless COMP

  39. Noiseless COMP

  40. Noiseless COMP

  41. Noiseless COMP

  42. Noisy COMP

  43. Noisy COMP If then =1 else =0

  44. Noisy COMP

  45. Noisy COMP

  46. Noisy COMP

  47. Noisy COMP

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