Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient...
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![Page 1: Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms Chun Lam Chan, Pak Hou Che and Sidharth.](https://reader035.fdocuments.net/reader035/viewer/2022062715/56649d785503460f94a5a27d/html5/thumbnails/1.jpg)
Non-adaptive probabilistic group testing with noisy measurements: Near-optimal
bounds with efficient algorithmsChun Lam Chan, Pak Hou Che and Sidharth Jaggi
The Chinese University of Hong Kong
Venkatesh Saligrama
Boston University
![Page 2: Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms Chun Lam Chan, Pak Hou Che and Sidharth.](https://reader035.fdocuments.net/reader035/viewer/2022062715/56649d785503460f94a5a27d/html5/thumbnails/2.jpg)
Non-adaptive probabilistic group testing with noisy measurements: Near-optimal
bounds with efficient algorithmsChun Lam Chan, Pak Hou Che and Sidharth Jaggi
The Chinese University of Hong Kong
Venkatesh Saligrama
Boston University
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![Page 3: Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms Chun Lam Chan, Pak Hou Che and Sidharth.](https://reader035.fdocuments.net/reader035/viewer/2022062715/56649d785503460f94a5a27d/html5/thumbnails/3.jpg)
Non-adaptive probabilistic group testing with noisy measurements: Near-optimal
bounds with efficient algorithmsChun Lam Chan, Pak Hou Che and Sidharth Jaggi
The Chinese University of Hong Kong
Venkatesh Saligrama
Boston University
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![Page 4: Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms Chun Lam Chan, Pak Hou Che and Sidharth.](https://reader035.fdocuments.net/reader035/viewer/2022062715/56649d785503460f94a5a27d/html5/thumbnails/4.jpg)
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Literature No error: [DR82], [DRR89] With small error ϵ:
Upper bound: [AS09], [SJ10]
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Literature No error: [DR82], [DRR89] With small error ϵ:
Upper bound: [AS09], [SJ10]
Lower bound: [Folklore]
![Page 6: Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms Chun Lam Chan, Pak Hou Che and Sidharth.](https://reader035.fdocuments.net/reader035/viewer/2022062715/56649d785503460f94a5a27d/html5/thumbnails/6.jpg)
Non-adaptive probabilistic group testing with noisy measurements: Near-optimal
bounds with efficient algorithms
![Page 7: Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms Chun Lam Chan, Pak Hou Che and Sidharth.](https://reader035.fdocuments.net/reader035/viewer/2022062715/56649d785503460f94a5a27d/html5/thumbnails/7.jpg)
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Algorithms motivated by Compressive Sensing Combinatorial Basis Pursuit (CBP) Combinatorial Orthogonal Matching Pursuit
(COMP)
![Page 8: Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms Chun Lam Chan, Pak Hou Che and Sidharth.](https://reader035.fdocuments.net/reader035/viewer/2022062715/56649d785503460f94a5a27d/html5/thumbnails/8.jpg)
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Noiseless CBP
n-dd
![Page 9: Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms Chun Lam Chan, Pak Hou Che and Sidharth.](https://reader035.fdocuments.net/reader035/viewer/2022062715/56649d785503460f94a5a27d/html5/thumbnails/9.jpg)
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Noiseless CBP
n-dd
Discard
![Page 10: Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms Chun Lam Chan, Pak Hou Che and Sidharth.](https://reader035.fdocuments.net/reader035/viewer/2022062715/56649d785503460f94a5a27d/html5/thumbnails/10.jpg)
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Noiseless CBP Sample g times to form a
group
n-dd
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Noiseless CBP Sample g times to form a
group
n-dd
![Page 12: Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms Chun Lam Chan, Pak Hou Che and Sidharth.](https://reader035.fdocuments.net/reader035/viewer/2022062715/56649d785503460f94a5a27d/html5/thumbnails/12.jpg)
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Noiseless CBP Sample g times to form a
group
n-dd
![Page 13: Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms Chun Lam Chan, Pak Hou Che and Sidharth.](https://reader035.fdocuments.net/reader035/viewer/2022062715/56649d785503460f94a5a27d/html5/thumbnails/13.jpg)
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Noiseless CBP Sample g times to form a
group
n-dd
![Page 14: Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms Chun Lam Chan, Pak Hou Che and Sidharth.](https://reader035.fdocuments.net/reader035/viewer/2022062715/56649d785503460f94a5a27d/html5/thumbnails/14.jpg)
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Noiseless CBP Sample g times to form a
group
Total non-defective items drawn:
n-dd
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Noiseless CBP Sample g times to form a
group
Total non-defective items drawn:
Coupon collection:
n-dd
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Noiseless CBP Sample g times to form a
group
Total non-defective items drawn:
Coupon collection:
Conclusion:
n-dd
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Noisy CBP
n-dd
![Page 18: Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms Chun Lam Chan, Pak Hou Che and Sidharth.](https://reader035.fdocuments.net/reader035/viewer/2022062715/56649d785503460f94a5a27d/html5/thumbnails/18.jpg)
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Noisy CBP
n-dd
![Page 19: Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms Chun Lam Chan, Pak Hou Che and Sidharth.](https://reader035.fdocuments.net/reader035/viewer/2022062715/56649d785503460f94a5a27d/html5/thumbnails/19.jpg)
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Noisy CBP
n-dd
![Page 20: Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms Chun Lam Chan, Pak Hou Che and Sidharth.](https://reader035.fdocuments.net/reader035/viewer/2022062715/56649d785503460f94a5a27d/html5/thumbnails/20.jpg)
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Noisy CBP
n-dd
![Page 21: Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms Chun Lam Chan, Pak Hou Che and Sidharth.](https://reader035.fdocuments.net/reader035/viewer/2022062715/56649d785503460f94a5a27d/html5/thumbnails/21.jpg)
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Noiseless COMP
![Page 22: Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms Chun Lam Chan, Pak Hou Che and Sidharth.](https://reader035.fdocuments.net/reader035/viewer/2022062715/56649d785503460f94a5a27d/html5/thumbnails/22.jpg)
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Noiseless COMP
![Page 23: Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms Chun Lam Chan, Pak Hou Che and Sidharth.](https://reader035.fdocuments.net/reader035/viewer/2022062715/56649d785503460f94a5a27d/html5/thumbnails/23.jpg)
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Noiseless COMP
![Page 24: Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms Chun Lam Chan, Pak Hou Che and Sidharth.](https://reader035.fdocuments.net/reader035/viewer/2022062715/56649d785503460f94a5a27d/html5/thumbnails/24.jpg)
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Noiseless COMP
![Page 25: Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms Chun Lam Chan, Pak Hou Che and Sidharth.](https://reader035.fdocuments.net/reader035/viewer/2022062715/56649d785503460f94a5a27d/html5/thumbnails/25.jpg)
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Noiseless COMP
![Page 26: Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms Chun Lam Chan, Pak Hou Che and Sidharth.](https://reader035.fdocuments.net/reader035/viewer/2022062715/56649d785503460f94a5a27d/html5/thumbnails/26.jpg)
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Noisy COMP
![Page 27: Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms Chun Lam Chan, Pak Hou Che and Sidharth.](https://reader035.fdocuments.net/reader035/viewer/2022062715/56649d785503460f94a5a27d/html5/thumbnails/27.jpg)
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Noisy COMP
![Page 28: Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms Chun Lam Chan, Pak Hou Che and Sidharth.](https://reader035.fdocuments.net/reader035/viewer/2022062715/56649d785503460f94a5a27d/html5/thumbnails/28.jpg)
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Noisy COMP
![Page 29: Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms Chun Lam Chan, Pak Hou Che and Sidharth.](https://reader035.fdocuments.net/reader035/viewer/2022062715/56649d785503460f94a5a27d/html5/thumbnails/29.jpg)
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Noisy COMP
![Page 30: Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms Chun Lam Chan, Pak Hou Che and Sidharth.](https://reader035.fdocuments.net/reader035/viewer/2022062715/56649d785503460f94a5a27d/html5/thumbnails/30.jpg)
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Noisy COMP
![Page 31: Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms Chun Lam Chan, Pak Hou Che and Sidharth.](https://reader035.fdocuments.net/reader035/viewer/2022062715/56649d785503460f94a5a27d/html5/thumbnails/31.jpg)
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Noisy COMP
![Page 32: Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms Chun Lam Chan, Pak Hou Che and Sidharth.](https://reader035.fdocuments.net/reader035/viewer/2022062715/56649d785503460f94a5a27d/html5/thumbnails/32.jpg)
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Noisy COMP
![Page 33: Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms Chun Lam Chan, Pak Hou Che and Sidharth.](https://reader035.fdocuments.net/reader035/viewer/2022062715/56649d785503460f94a5a27d/html5/thumbnails/33.jpg)
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Simulations
0 100 200 300 400 500 600 700 8000
1
Experimental; q=0
Theoretical-lower; q=0
Theoretical-upper;q=0
number of tests (T)
succ
ess
rate
![Page 34: Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms Chun Lam Chan, Pak Hou Che and Sidharth.](https://reader035.fdocuments.net/reader035/viewer/2022062715/56649d785503460f94a5a27d/html5/thumbnails/34.jpg)
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Simulations
0 500 1000 1500 2000 2500 30000
1
Experimental; q=0
Experimental; q=0.1
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
number of tests (T)
succ
ess
rate
![Page 35: Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms Chun Lam Chan, Pak Hou Che and Sidharth.](https://reader035.fdocuments.net/reader035/viewer/2022062715/56649d785503460f94a5a27d/html5/thumbnails/35.jpg)
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Summary
CBP COMP
Noiseless
Noisy
With small error ,
![Page 36: Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms Chun Lam Chan, Pak Hou Che and Sidharth.](https://reader035.fdocuments.net/reader035/viewer/2022062715/56649d785503460f94a5a27d/html5/thumbnails/36.jpg)
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End
Thanks
![Page 37: Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms Chun Lam Chan, Pak Hou Che and Sidharth.](https://reader035.fdocuments.net/reader035/viewer/2022062715/56649d785503460f94a5a27d/html5/thumbnails/37.jpg)
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Noiseless COMP
x 0 0 1 0 0 0 1 0 0
M y
0 1 1 1 0 0 0 0 0 10 0 0 1 0 0 1 0 0 10 1 0 0 0 0 0 0 1 01 1 1 0 0 0 1 1 0 10 0 1 1 0 1 1 0 0 10 0 0 0 1 0 0 1 1 0
0 0 1 1 0 1 1 0 0 1
![Page 38: Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms Chun Lam Chan, Pak Hou Che and Sidharth.](https://reader035.fdocuments.net/reader035/viewer/2022062715/56649d785503460f94a5a27d/html5/thumbnails/38.jpg)
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x 0 0 1 0 0 0 1 0 0
M y
0 1 1 1 0 0 0 0 0 10 0 0 1 0 0 1 0 0 10 1 0 0 0 0 0 0 1 01 1 1 0 0 0 1 1 0 10 0 1 1 0 1 1 0 0 10 0 0 0 1 0 0 1 1 0
0 0 1 1 0 1 1 0 0 1
0 10 11 0 x90 1 → 00 11 00 1
Noiseless COMP
![Page 39: Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms Chun Lam Chan, Pak Hou Che and Sidharth.](https://reader035.fdocuments.net/reader035/viewer/2022062715/56649d785503460f94a5a27d/html5/thumbnails/39.jpg)
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Noiseless COMP
x 0 0 1 0 0 0 1 0 0
M y
0 1 1 1 0 0 0 0 0 10 0 0 1 0 0 1 0 0 10 1 0 0 0 0 0 0 1 01 1 1 0 0 0 1 1 0 10 0 1 1 0 1 1 0 0 10 0 0 0 1 0 0 1 1 0
0 0 1 1 0 1 1 0 0 1
0 01 10 0 x71 1 → 11 10 01 1
![Page 40: Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms Chun Lam Chan, Pak Hou Che and Sidharth.](https://reader035.fdocuments.net/reader035/viewer/2022062715/56649d785503460f94a5a27d/html5/thumbnails/40.jpg)
40
Noiseless COMP
x 0 0 1 0 0 0 1 0 0
M y
0 1 1 1 0 0 0 0 0 10 0 0 1 0 0 1 0 0 10 1 0 0 0 0 0 0 1 01 1 1 0 0 0 1 1 0 10 0 1 1 0 1 1 0 0 10 0 0 0 1 0 0 1 1 0
0 0 1 1 0 1 1 0 0 1
1 11 10 0 x40 1 → 11 10 01 1
![Page 41: Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms Chun Lam Chan, Pak Hou Che and Sidharth.](https://reader035.fdocuments.net/reader035/viewer/2022062715/56649d785503460f94a5a27d/html5/thumbnails/41.jpg)
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Noiseless COMP
x 0 0 1 0 0 0 1 0 0
M y0 1 1 1 0 0 0 0 0 10 0 0 1 0 0 1 0 0 10 1 0 0 0 0 0 0 1 01 1 1 0 0 0 1 1 0 10 0 1 1 0 1 1 0 0 10 0 0 0 1 0 0 1 1 00 0 1 1 0 1 1 0 0 1
1 1 0 0 0 11 1 1 1 0 10 0 x4 0 0 x7 1 0 x9
(a) 0 1 → 1 (b) 1 1 → 1 (c) 0 1 → 01 1 1 1 0 10 0 0 0 1 01 1 1 1 0 1
![Page 42: Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms Chun Lam Chan, Pak Hou Che and Sidharth.](https://reader035.fdocuments.net/reader035/viewer/2022062715/56649d785503460f94a5a27d/html5/thumbnails/42.jpg)
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Noisy COMPx 0 0 1 0 0 0 1 0 0
M y ν ŷ0 1 0 1 0 0 0 0 0 0 0 00 0 0 1 0 0 1 0 0 1 1 00 1 0 0 0 0 0 0 1 0 1 11 1 1 0 0 0 1 1 1 1 + 1 → 00 1 1 1 0 1 0 0 0 1 0 10 0 0 0 1 0 0 1 1 0 0 00 0 1 1 0 1 1 0 0 1 0 1
0 00 00 11 01 10 01 1
![Page 43: Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms Chun Lam Chan, Pak Hou Che and Sidharth.](https://reader035.fdocuments.net/reader035/viewer/2022062715/56649d785503460f94a5a27d/html5/thumbnails/43.jpg)
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Noisy COMPx 0 0 1 0 0 0 1 0 0
M y ν ŷ0 1 0 1 0 0 0 0 0 0 0 00 0 0 1 0 0 1 0 0 1 1 00 1 0 0 0 0 0 0 1 0 1 11 1 1 0 0 0 1 1 1 1 + 1 → 00 1 1 1 0 1 0 0 0 1 0 10 0 0 0 1 0 0 1 1 0 0 00 0 1 1 0 1 1 0 0 1 0 1
0 00 00 1 x31 0 → 11 10 01 1
If then =1 else =0
![Page 44: Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms Chun Lam Chan, Pak Hou Che and Sidharth.](https://reader035.fdocuments.net/reader035/viewer/2022062715/56649d785503460f94a5a27d/html5/thumbnails/44.jpg)
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Noisy COMPx 0 0 1 0 0 0 1 0 0
M y ν ŷ0 1 0 1 0 0 0 0 0 0 0 00 0 0 1 0 0 1 0 0 1 1 00 1 0 0 0 0 0 0 1 0 1 11 1 1 0 0 0 1 1 1 1 + 1 → 00 1 1 1 0 1 0 0 0 1 0 10 0 0 0 1 0 0 1 1 0 0 00 0 1 1 0 1 1 0 0 1 0 1
1 00 01 1 x2
1 0 → 1
1 10 00 1
![Page 45: Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms Chun Lam Chan, Pak Hou Che and Sidharth.](https://reader035.fdocuments.net/reader035/viewer/2022062715/56649d785503460f94a5a27d/html5/thumbnails/45.jpg)
45
Noisy COMPx 0 0 1 0 0 0 1 0 0
M y ν ŷ0 1 0 1 0 0 0 0 0 0 0 00 0 0 1 0 0 1 0 0 1 1 00 1 0 0 0 0 0 0 1 0 1 11 1 1 0 0 0 1 1 1 1 + 1 → 00 1 1 1 0 1 0 0 0 1 0 10 0 0 0 1 0 0 1 1 0 0 00 0 1 1 0 1 1 0 0 1 0 1
0 01 00 1 x71 0 → 00 10 01 1
![Page 46: Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms Chun Lam Chan, Pak Hou Che and Sidharth.](https://reader035.fdocuments.net/reader035/viewer/2022062715/56649d785503460f94a5a27d/html5/thumbnails/46.jpg)
46
Noisy COMP
x 0 0 1 0 0 0 1 0 0
M y ν ŷ0 1 0 1 0 0 0 0 0 0 0 00 0 0 1 0 0 1 0 0 1 1 00 1 0 0 0 0 0 0 1 0 1 11 1 1 0 0 0 1 1 1 1 + 1 → 00 1 1 1 0 1 0 0 0 1 0 10 0 0 0 1 0 0 1 1 0 0 00 0 1 1 0 1 1 0 0 1 0 1
1 0 0 0 0 00 0 0 0 1 01 1 x2 0 1 x3 0 1 x7
(a) 1 0 → 1 (b) 1 0 → 1 (c) 1 0 → 01 1 1 1 0 10 0 0 0 0 00 1 1 1 1 1
![Page 47: Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms Chun Lam Chan, Pak Hou Che and Sidharth.](https://reader035.fdocuments.net/reader035/viewer/2022062715/56649d785503460f94a5a27d/html5/thumbnails/47.jpg)
47
Noisy COMP
x 0 0 1 0 0 0 1 0 0
M y ν ŷ0 1 0 1 0 0 0 0 0 0 0 00 0 0 1 0 0 1 0 0 1 1 00 1 0 0 0 0 0 0 1 0 1 11 1 1 0 0 0 1 1 1 1 + 1 → 00 1 1 1 0 1 0 0 0 1 0 10 0 0 0 1 0 0 1 1 0 0 00 0 1 1 0 1 1 0 0 1 0 1
1 0 0 0 0 00 0 0 0 1 01 1 x2 0 1 x3 0 1 x7
(a) 1 0 → 1 (b) 1 0 → 1 (c) 1 0 → 01 1 1 1 0 10 0 0 0 0 00 1 1 1 1 1