Nonadaptive probabilistic group testing with noisy measurements Nearoptimal
Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms Chun Lam Chan, Pak Hou Che and Sidharth Jaggi Venkatesh Saligrama The Chinese University of Hong Kong Boston University
n-d d Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms Chun Lam Chan, Pak Hou Che and Sidharth Jaggi Venkatesh Saligrama The Chinese University of Hong Kong Boston University
n-d d Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms Chun Lam Chan, Pak Hou Che and Sidharth Jaggi Venkatesh Saligrama The Chinese University of Hong Kong Boston University
Literature � No error: [DR 82], [DRR 89] � With small error ϵ: � Upper bound: [AS 09], [SJ 10] 4
Literature � No error: [DR 82], [DRR 89] � With small error ϵ: � Upper bound: [AS 09], [SJ 10] � Lower bound: [Folklore] 5
Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms
Algorithms motivated by Compressive Sensing � Combinatorial Basis Pursuit (CBP) � Combinatorial Orthogonal Matching Pursuit (COMP) 7
Noiseless CBP n-d d 8
Noiseless CBP Discard n-d d 9
Noiseless CBP � n-d d 10 Sample g times to form a group
Noiseless CBP � n-d d 11 Sample g times to form a group
Noiseless CBP � n-d d 12 Sample g times to form a group
Noiseless CBP � n-d d 13 Sample g times to form a group
Noiseless CBP n-d d 14 � Sample g times to form a group � Total non-defective items drawn:
Noiseless CBP � Sample g times to form a group � Total non-defective items drawn: � Coupon collection: n-d d 15
Noiseless CBP � Sample g times to form a group � Total non-defective items drawn: � Coupon collection: � Conclusion: n-d d 16
Noisy CBP n-d d 17
Noisy CBP n-d d 18
Noisy CBP n-d d 19
Noisy CBP n-d d 20
Noiseless COMP 21
Noiseless COMP 22
Noiseless COMP 23
Noiseless COMP 24
Noiseless COMP 25
Noisy COMP 26
Noisy COMP 27
Noisy COMP 28
Noisy COMP 29
Noisy COMP 30
Noisy COMP 31
Noisy COMP 32
Simulations 1 success rate Experimental; q=0 Theoretical-lower; q=0 Theoreticalupper; q=0 0 0 100 200 300 400 number of tests (T) 33 500 600 700 800
Simulations 1 Experimental; q=0. 1 success rate Experimental; q=0. 2 Theoretical-lower; q=0 Theoretical-lowerl; q=0. 1 Theoretical-lower; q=0. 2 Theoretical-upper; q=0 Theoretical-lower; q=0. 1 Theoretical-lower; q=0. 2 0 0 34 500 1000 1500 number of tests (T) 2000 2500 3000
Summary � With small error , CBP Noiseles s Noisy 35 COMP
End Thanks 36
Noiseless COMP x 0 0 1 0 0 0 37 0 1 1 0 0 0 1 1 0 1 0 1 M 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 1 0 y 1 1 0 1
Noiseless COMP x 0 0 0 0 1 0 1 1 0 0 1 1 0 0 1 M 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 1 0 y 1 1 0 1 0 38 1 1 0 x 9 1 → 0 1
Noiseless COMP x 0 0 1 0 0 0 39 0 1 1 0 0 0 1 1 0 1 0 0 0 1 1 1 0 0 1 M 0 0 0 0 0 1 0 1 0 1 0 x 7 1 → 1 1 0 1 0 1 0 0 0 0 1 0 y 1 1 0 1
Noiseless COMP x 0 0 1 0 0 0 1 1 0 0 1 40 1 1 0 x 4 1 → 1 1 0 1 0 1 1 0 0 1 1 0 0 1 M 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 1 0 y 1 1 0 1
Noiseless COMP x 0 0 1 0 0 0 1 1 0 (a) 0 1 41 1 1 0 x 4 1 → 1 1 0 0 0 1 1 1 0 0 1 M 0 0 0 1 0 (b) 1 1 0 0 0 0 1 0 1 1 0 0 0 1 0 x 7 1 → 1 1 0 0 1 0 y 1 1 0 1 0 0 1 (c) 0 0 1 1 0 x 9 1 → 0 1
Noisy COMP x 42 0 0 1 0 0 0 1 0 1 1 1 0 0 0 1 1 0 0 1 M 0 0 0 1 0 1 0 0 0 1 1 0 0 1 0 1 0 0 0 0 1 1 0 y 0 1 1 0 1 + ν 0 1 1 1 0 0 0 → ŷ 0 0 1 0 1
Noisy COMP x 43 0 0 1 0 0 0 1 0 1 1 1 0 0 0 1 1 0 0 1 M 0 0 0 1 0 1 0 0 0 1 1 0 0 1 0 1 0 0 0 0 1 1 0 x 3 → 1 y 0 1 1 0 1 + ν 0 1 1 1 0 0 0 → ŷ 0 0 1 0 1
Noisy COMP x 44 1 0 1 0 0 0 1 0 0 0 1 0 1 1 1 0 0 0 1 1 0 1 x 2 → 1 0 0 1 0 1 M 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 y 0 1 1 0 1 + ν 0 1 1 1 0 0 0 → ŷ 0 0 1 0 1
Noisy COMP x 0 0 1 0 0 0 1 0 1 1 1 0 0 0 1 1 0 0 1 M 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 y 0 1 1 0 1 + ν 0 1 1 1 0 0 1 45 → 0 0 1 0 1 ŷ 0 0 1 0 1 x 7 → 0
Noisy COMP x 0 0 1 0 0 0 1 (a) 1 1 0 0 46 1 0 1 1 1 0 0 1 x 2 0 → 1 1 0 1 0 0 0 1 1 1 0 0 1 M 0 0 0 0 0 1 0 1 0 0 0 (b) 1 1 0 1 0 0 0 1 1 0 0 0 1 x 3 0 → 1 1 0 1 ŷ y ν 0 0 0 1 1 1 + 1 → 0 1 0 0 0 1 0 1 0 (c) 1 0 0 1 x 7 0 → 0 1
Noisy COMP x 0 0 1 0 0 0 1 (a) 1 1 0 0 47 1 0 1 1 1 0 0 1 x 2 0 → 1 1 0 1 0 0 0 1 1 1 0 0 1 M 0 0 0 0 0 1 0 1 0 0 0 (b) 1 1 0 1 0 0 0 1 1 0 0 0 1 x 3 0 → 1 1 0 1 ŷ y ν 0 0 0 1 1 1 + 1 → 0 1 0 0 0 1 0 1 0 (c) 1 0 0 1 x 7 0 → 0 1
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