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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

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

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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. - PowerPoint PPT Presentation

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Page 1: 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 algorithmsChun Lam Chan, Pak Hou Che and Sidharth Jaggi

The Chinese University of Hong KongVenkatesh Saligrama

Boston University

Page 2: 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 algorithmsChun Lam Chan, Pak Hou Che and Sidharth Jaggi

The Chinese University of Hong KongVenkatesh Saligrama

Boston University

n-dd

Page 3: 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 algorithmsChun Lam Chan, Pak Hou Che and Sidharth Jaggi

The Chinese University of Hong KongVenkatesh Saligrama

Boston University

n-dd

Page 4: Chun Lam Chan , Pak  Hou Che  and  Sidharth Jaggi The Chinese University of Hong Kong

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Literature No error: [DR82], [DRR89] With small error ϵ:

Upper bound: [AS09], [SJ10]

Page 5: Chun Lam Chan , Pak  Hou Che  and  Sidharth Jaggi The Chinese University of Hong Kong

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Literature No error: [DR82], [DRR89] With small error ϵ:

Upper bound: [AS09], [SJ10]

Lower bound: [Folklore]

Page 6: 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

Page 7: Chun Lam Chan , Pak  Hou Che  and  Sidharth Jaggi The Chinese University of Hong Kong

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Algorithms motivated by Compressive Sensing Combinatorial Basis Pursuit (CBP) Combinatorial Orthogonal Matching Pursuit

(COMP)

Page 8: Chun Lam Chan , Pak  Hou Che  and  Sidharth Jaggi The Chinese University of Hong Kong

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Noiseless CBP

n-dd

Page 9: Chun Lam Chan , Pak  Hou Che  and  Sidharth Jaggi The Chinese University of Hong Kong

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Noiseless CBP

n-dd

Discard

Page 10: Chun Lam Chan , Pak  Hou Che  and  Sidharth Jaggi The Chinese University of Hong Kong

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Noiseless CBP Sample g times to form a

group

n-dd

Page 11: Chun Lam Chan , Pak  Hou Che  and  Sidharth Jaggi The Chinese University of Hong Kong

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Noiseless CBP Sample g times to form a

group

n-dd

Page 12: Chun Lam Chan , Pak  Hou Che  and  Sidharth Jaggi The Chinese University of Hong Kong

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Noiseless CBP Sample g times to form a

group

n-dd

Page 13: Chun Lam Chan , Pak  Hou Che  and  Sidharth Jaggi The Chinese University of Hong Kong

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Noiseless CBP Sample g times to form a

group

n-dd

Page 14: Chun Lam Chan , Pak  Hou Che  and  Sidharth Jaggi The Chinese University of Hong Kong

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Noiseless CBP Sample g times to form a

group

Total non-defective items drawn:

n-dd

Page 15: Chun Lam Chan , Pak  Hou Che  and  Sidharth Jaggi The Chinese University of Hong Kong

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Noiseless CBP Sample g times to form a

group

Total non-defective items drawn:

Coupon collection:

n-dd

Page 16: Chun Lam Chan , Pak  Hou Che  and  Sidharth Jaggi The Chinese University of Hong Kong

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Noiseless CBP Sample g times to form a

group

Total non-defective items drawn:

Coupon collection:

Conclusion:

n-dd

Page 17: Chun Lam Chan , Pak  Hou Che  and  Sidharth Jaggi The Chinese University of Hong Kong

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Noisy CBP

n-dd

Page 18: Chun Lam Chan , Pak  Hou Che  and  Sidharth Jaggi The Chinese University of Hong Kong

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Noisy CBP

n-dd

Page 19: Chun Lam Chan , Pak  Hou Che  and  Sidharth Jaggi The Chinese University of Hong Kong

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Noisy CBP

n-dd

Page 20: Chun Lam Chan , Pak  Hou Che  and  Sidharth Jaggi The Chinese University of Hong Kong

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Noisy CBP

n-dd

Page 21: Chun Lam Chan , Pak  Hou Che  and  Sidharth Jaggi The Chinese University of Hong Kong

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Noiseless COMP

Page 22: Chun Lam Chan , Pak  Hou Che  and  Sidharth Jaggi The Chinese University of Hong Kong

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Noiseless COMP

Page 23: Chun Lam Chan , Pak  Hou Che  and  Sidharth Jaggi The Chinese University of Hong Kong

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Noiseless COMP

Page 24: Chun Lam Chan , Pak  Hou Che  and  Sidharth Jaggi The Chinese University of Hong Kong

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Noiseless COMP

Page 25: Chun Lam Chan , Pak  Hou Che  and  Sidharth Jaggi The Chinese University of Hong Kong

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Noiseless COMP

Page 26: Chun Lam Chan , Pak  Hou Che  and  Sidharth Jaggi The Chinese University of Hong Kong

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Noisy COMP

Page 27: Chun Lam Chan , Pak  Hou Che  and  Sidharth Jaggi The Chinese University of Hong Kong

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Noisy COMP

Page 28: Chun Lam Chan , Pak  Hou Che  and  Sidharth Jaggi The Chinese University of Hong Kong

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Noisy COMP

 

Page 29: Chun Lam Chan , Pak  Hou Che  and  Sidharth Jaggi The Chinese University of Hong Kong

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Noisy COMP

Page 30: Chun Lam Chan , Pak  Hou Che  and  Sidharth Jaggi The Chinese University of Hong Kong

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Noisy COMP

Page 31: Chun Lam Chan , Pak  Hou Che  and  Sidharth Jaggi The Chinese University of Hong Kong

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Noisy COMP

Page 32: Chun Lam Chan , Pak  Hou Che  and  Sidharth Jaggi The Chinese University of Hong Kong

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Noisy COMP

Page 33: Chun Lam Chan , Pak  Hou Che  and  Sidharth Jaggi The Chinese University of Hong Kong

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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 r

ate

Page 34: Chun Lam Chan , Pak  Hou Che  and  Sidharth Jaggi The Chinese University of Hong Kong

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Simulations

0 500 1000 1500 2000 2500 30000

1

Experimental; q=0Experimental; q=0.1Experimental; q=0.2Theoretical-lower; q=0Theoretical-lowerl; q=0.1Theoretical-lower; q=0.2Theoretical-upper;q=0Theoretical-lower; q=0.1Theoretical-lower; q=0.2

number of tests (T)

succ

ess r

ate

Page 35: Chun Lam Chan , Pak  Hou Che  and  Sidharth Jaggi The Chinese University of Hong Kong

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Summary

CBP COMPNoiselessNoisy

With small error ,

Page 36: Chun Lam Chan , Pak  Hou Che  and  Sidharth Jaggi The Chinese University of Hong Kong

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End

Thanks

Page 37: Chun Lam Chan , Pak  Hou Che  and  Sidharth Jaggi The Chinese University of Hong Kong

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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

Page 38: Chun Lam Chan , Pak  Hou Che  and  Sidharth Jaggi The Chinese University of Hong Kong

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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

0 10 11 0 x90 1 → 00 11 00 1

Noiseless COMP

Page 39: Chun Lam Chan , Pak  Hou Che  and  Sidharth Jaggi The Chinese University of Hong Kong

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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

0 01 10 0 x71 1 → 11 10 01 1

Page 40: Chun Lam Chan , Pak  Hou Che  and  Sidharth Jaggi The Chinese University of Hong Kong

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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 11 10 0 x40 1 → 11 10 01 1

Page 41: Chun Lam Chan , Pak  Hou Che  and  Sidharth Jaggi The Chinese University of Hong Kong

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

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

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

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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 x21 0 → 11 10 00 1

Page 45: Chun Lam Chan , Pak  Hou Che  and  Sidharth Jaggi The Chinese University of Hong Kong

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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 01 00 1 x71 0 → 00 10 01 1

Page 46: Chun Lam Chan , Pak  Hou Che  and  Sidharth Jaggi The Chinese University of Hong Kong

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

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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 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