Gossip-based Truth Discovery Motivation Motivating Examples - - PowerPoint PPT Presentation

Gossip-based Truth Discovery Zhiying Xu Introduction

Motivation Motivating Examples

Problem Formulation Computational Complexity Proposed Algorithms

Exact Algorithm Approximation Algorithms

Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

Future Work

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Gossip-based Truth Discovery

Zhiying Xu June 4, 2017

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Gossip-based Truth Discovery Zhiying Xu Introduction

Motivation Motivating Examples

Problem Formulation Computational Complexity Proposed Algorithms

Exact Algorithm Approximation Algorithms

Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

Future Work

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline

1 Introduction

Motivation Motivating Examples

2 Problem Formulation 3 Computational Complexity 4 Proposed Algorithms

Exact Algorithm Approximation Algorithms

5 Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

6 Future Work

2 / 36

Gossip-based Truth Discovery Zhiying Xu Introduction

Motivation Motivating Examples

Problem Formulation Computational Complexity Proposed Algorithms

Exact Algorithm Approximation Algorithms

Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

Future Work

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline

1 Introduction

Motivation Motivating Examples

2 Problem Formulation 3 Computational Complexity 4 Proposed Algorithms

Exact Algorithm Approximation Algorithms

5 Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

6 Future Work

3 / 36

Gossip-based Truth Discovery Zhiying Xu Introduction

Motivation Motivating Examples

Problem Formulation Computational Complexity Proposed Algorithms

Exact Algorithm Approximation Algorithms

Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

Future Work

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline

1 Introduction

Motivation Motivating Examples

2 Problem Formulation 3 Computational Complexity 4 Proposed Algorithms

Exact Algorithm Approximation Algorithms

5 Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

6 Future Work

4 / 36

Gossip-based Truth Discovery Zhiying Xu Introduction

Motivation Motivating Examples

Problem Formulation Computational Complexity Proposed Algorithms

Exact Algorithm Approximation Algorithms

Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

Future Work

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Gossip Algorithm

Gossip algorithms: schemes which distribute the computation burden and in which a node communicates with a randomly chosen neighbor.

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Gossip-based Truth Discovery Zhiying Xu Introduction

Motivation Motivating Examples

Problem Formulation Computational Complexity Proposed Algorithms

Exact Algorithm Approximation Algorithms

Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

Future Work

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Truth Discovery

Discover truth from noisy crowd sensing data Evaluate the reliability of sensors

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Gossip-based Truth Discovery Zhiying Xu Introduction

Motivation Motivating Examples

Problem Formulation Computational Complexity Proposed Algorithms

Exact Algorithm Approximation Algorithms

Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

Future Work

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline

1 Introduction

Motivation Motivating Examples

2 Problem Formulation 3 Computational Complexity 4 Proposed Algorithms

Exact Algorithm Approximation Algorithms

5 Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

6 Future Work

7 / 36

Gossip-based Truth Discovery Zhiying Xu Introduction

Motivation Motivating Examples

Problem Formulation Computational Complexity Proposed Algorithms

Exact Algorithm Approximation Algorithms

Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

Future Work

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

A Real-life Case

Whether the class is canceled?

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Gossip-based Truth Discovery Zhiying Xu Introduction

Motivation Motivating Examples

Problem Formulation Computational Complexity Proposed Algorithms

Exact Algorithm Approximation Algorithms

Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

Future Work

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline

1 Introduction

Motivation Motivating Examples

2 Problem Formulation 3 Computational Complexity 4 Proposed Algorithms

Exact Algorithm Approximation Algorithms

5 Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

6 Future Work

9 / 36

Gossip-based Truth Discovery Zhiying Xu Introduction

Motivation Motivating Examples

Problem Formulation Computational Complexity Proposed Algorithms

Exact Algorithm Approximation Algorithms

Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

Future Work

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Model

Definition (Problem Formulation) Given a crowd sensing model where N sensors make individual

• bservations X N×M ∈ {0, 1}N×M about a set of M variables,

determine the true value of these variables tM ∈ {0, 1}M which satisfies ⟨t, r⟩ = arg min

⟨t,r⟩

p (X|t, r) , where r N ∈ [0, 1] is the reliability of sensors.

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Gossip-based Truth Discovery Zhiying Xu Introduction

Motivation Motivating Examples

Problem Formulation Computational Complexity Proposed Algorithms

Exact Algorithm Approximation Algorithms

Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

Future Work

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Model

Definition (Problem Formulation) Given a crowd sensing model where N sensors make individual

• bservations X N×M ∈ {0, 1}N×M about a set of M variables,

determine the true value of these variables tM ∈ {0, 1}M which satisfies ⟨t, r⟩ = arg min

⟨t,r⟩

p (X|t, r) , where r N ∈ [0, 1] is the reliability of sensors. t, r are related to each other. There is no need for iteration by EM algorithm.

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Gossip-based Truth Discovery Zhiying Xu Introduction

Motivation Motivating Examples

Problem Formulation Computational Complexity Proposed Algorithms

Exact Algorithm Approximation Algorithms

Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

Future Work

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Objective Function

Using the relationship between t and r, We can simplify the previous problem into the optimization of the objective function t = arg min

t N

∑

i=1

f (xi, t) , where f (xi, t) denotes

||xi−t|| M

ln

M ||xi−t|| +

( 1 − ||xi−t||

M

) ln ( 1 −

M ||xi−t||

) .

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Gossip-based Truth Discovery Zhiying Xu Introduction

Motivation Motivating Examples

Problem Formulation Computational Complexity Proposed Algorithms

Exact Algorithm Approximation Algorithms

Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

Future Work

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Truth Discovery Strategy

All sensors are in a connected networks. Sensors have limited memory and can’t store much data. Each sensor communicates with a random neighbor asynchronously.

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Gossip-based Truth Discovery Zhiying Xu Introduction

Motivation Motivating Examples

Problem Formulation Computational Complexity Proposed Algorithms

Exact Algorithm Approximation Algorithms

Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

Future Work

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline

1 Introduction

Motivation Motivating Examples

2 Problem Formulation 3 Computational Complexity 4 Proposed Algorithms

Exact Algorithm Approximation Algorithms

5 Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

6 Future Work

13 / 36

Gossip-based Truth Discovery Zhiying Xu Introduction

Motivation Motivating Examples

Problem Formulation Computational Complexity Proposed Algorithms

Exact Algorithm Approximation Algorithms

Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

Future Work

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

NP Hardness of the Decision Version

Given a matrix X N×M, is there a vector tM which satisfies ∑N

i=1 f (xi, t) < C?

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Gossip-based Truth Discovery Zhiying Xu Introduction

Motivation Motivating Examples

Problem Formulation Computational Complexity Proposed Algorithms

Exact Algorithm Approximation Algorithms

Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

Future Work

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Proof of NP Hardness

Theorem Discovering the truth t from the observed matrix X is NP-hard. By reduction from 3 exact cover problem. Inspired by Cardinal, J., Fiorini, S. and Joret, G., 2012. Minimum entropy combinatorial optimization problems. Theory of Computing Systems, 51(1), pp.4-21.

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Gossip-based Truth Discovery Zhiying Xu Introduction

Motivation Motivating Examples

Problem Formulation Computational Complexity Proposed Algorithms

Exact Algorithm Approximation Algorithms

Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

Future Work

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Proof of NP Hardness

Proof: Step 1 3 exact cover: Given a set system (U, S), decide whether U can be covered using pairwise disjoint sets from S ⇓ minimum orientation defined on a concave function: Construct a graph by creating a gadget for each element in U. Given the graph, decide whether there is an

• rientation that satisfies ∑|V |

i=1 g

( d+

i

|E|

) < C1. Here g (·) is a concave function and d+

i

is the in-degree of the node i.

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Gossip-based Truth Discovery Zhiying Xu Introduction

Motivation Motivating Examples

Problem Formulation Computational Complexity Proposed Algorithms

Exact Algorithm Approximation Algorithms

Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

Future Work

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Proof of NP Hardness

Proof: Step 2 minimum orientation defined on a concave function: Given the graph, decide whether there is an

• rientation that satisfies ∑|V |

i=1 g

( d+

i

|E|

) < C1. Here g (·) is a concave function and d+

i

is the in-degree of the node i. ⇓ Truth Discovery: Covert the graph into a matrix X, decide whether there is a vector tM which satisfies ∑N

i=1 f (xi, t) < C2.

X = ancillary part + graph part.

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Gossip-based Truth Discovery Zhiying Xu Introduction

Motivation Motivating Examples

Problem Formulation Computational Complexity Proposed Algorithms

Exact Algorithm Approximation Algorithms

Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

Future Work

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline

1 Introduction

Motivation Motivating Examples

2 Problem Formulation 3 Computational Complexity 4 Proposed Algorithms

Exact Algorithm Approximation Algorithms

5 Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

6 Future Work

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Gossip-based Truth Discovery Zhiying Xu Introduction

Motivation Motivating Examples

Problem Formulation Computational Complexity Proposed Algorithms

Exact Algorithm Approximation Algorithms

Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

Future Work

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline

1 Introduction

Motivation Motivating Examples

2 Problem Formulation 3 Computational Complexity 4 Proposed Algorithms

Exact Algorithm Approximation Algorithms

5 Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

6 Future Work

19 / 36

Gossip-based Truth Discovery Zhiying Xu Introduction

Motivation Motivating Examples

Problem Formulation Computational Complexity Proposed Algorithms

Exact Algorithm Approximation Algorithms

Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

Future Work

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

The Complexity of Exact Algorithm

Theorem The complexity of the exact algorithm is Θ ( 2rank(X)) .

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Gossip-based Truth Discovery Zhiying Xu Introduction

Motivation Motivating Examples

Problem Formulation Computational Complexity Proposed Algorithms

Exact Algorithm Approximation Algorithms

Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

Future Work

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

The Complexity of Exact Algorithm

Theorem The complexity of the exact algorithm is Θ ( 2rank(X)) . The base vectors can be obtained in polynomial time. The truth vector t is a combination of the base vectors of the observed vectors xi.

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Gossip-based Truth Discovery Zhiying Xu Introduction

Motivation Motivating Examples

Problem Formulation Computational Complexity Proposed Algorithms

Exact Algorithm Approximation Algorithms

Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

Future Work

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Exact Algorithm

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Gossip-based Truth Discovery Zhiying Xu Introduction

Motivation Motivating Examples

Problem Formulation Computational Complexity Proposed Algorithms

Exact Algorithm Approximation Algorithms

Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

Future Work

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline

1 Introduction

Motivation Motivating Examples

2 Problem Formulation 3 Computational Complexity 4 Proposed Algorithms

Exact Algorithm Approximation Algorithms

5 Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

6 Future Work

22 / 36

Gossip-based Truth Discovery Zhiying Xu Introduction

Motivation Motivating Examples

Problem Formulation Computational Complexity Proposed Algorithms

Exact Algorithm Approximation Algorithms

Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

Future Work

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Approximation Algorithm

Theorem The approximation algorithm achieves an approximation ratio of 1.7.

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Gossip-based Truth Discovery Zhiying Xu Introduction

Motivation Motivating Examples

Problem Formulation Computational Complexity Proposed Algorithms

Exact Algorithm Approximation Algorithms

Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

Future Work

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Approximation Algorithm

Theorem The approximation algorithm achieves an approximation ratio of 1.7. The approximation ratio is an upper bound, for the worse case is difficult to find. Use triangle inequality f (x, y) + f (y, z) > f (x, z). The complexity is Θ ( n2)

23 / 36

Gossip-based Truth Discovery Zhiying Xu Introduction

Motivation Motivating Examples

Problem Formulation Computational Complexity Proposed Algorithms

Exact Algorithm Approximation Algorithms

Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

Future Work

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Approximation Algorithm

24 / 36

Gossip-based Truth Discovery Zhiying Xu Introduction

Motivation Motivating Examples

Problem Formulation Computational Complexity Proposed Algorithms

Exact Algorithm Approximation Algorithms

Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

Future Work

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline

1 Introduction

Motivation Motivating Examples

2 Problem Formulation 3 Computational Complexity 4 Proposed Algorithms

Exact Algorithm Approximation Algorithms

5 Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

6 Future Work

25 / 36

Gossip-based Truth Discovery Zhiying Xu Introduction

Motivation Motivating Examples

Problem Formulation Computational Complexity Proposed Algorithms

Exact Algorithm Approximation Algorithms

Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

Future Work

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline

1 Introduction

Motivation Motivating Examples

2 Problem Formulation 3 Computational Complexity 4 Proposed Algorithms

Exact Algorithm Approximation Algorithms

5 Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

6 Future Work

26 / 36

Gossip-based Truth Discovery Zhiying Xu Introduction

Motivation Motivating Examples

Problem Formulation Computational Complexity Proposed Algorithms

Exact Algorithm Approximation Algorithms

Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

Future Work

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Decentralized Exact Algorithm

It’s hard to calculate the base vectors in a decentralized ways, so we decide to try every vector in {0, 1}M There is a trade-off between run time and accuracy. run time: 2M 3 log ϵ−1 log λ2 (W1)−1 W1 = I − 1 2nD + P + PT 2n Di =

n

∑

j=1

[Pij + Pji] accuracy: 1 + 2ϵ

27 / 36

Gossip-based Truth Discovery Zhiying Xu Introduction

Motivation Motivating Examples

Problem Formulation Computational Complexity Proposed Algorithms

Exact Algorithm Approximation Algorithms

Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

Future Work

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Decentralized Exact Algorithm

28 / 36

Gossip-based Truth Discovery Zhiying Xu Introduction

Motivation Motivating Examples

Problem Formulation Computational Complexity Proposed Algorithms

Exact Algorithm Approximation Algorithms

Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

Future Work

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

A Fast Algorithm for 1-median Problem

Using triangle inequality in metric space and Chebyshev Inequility Inspired by Indyk, P., 1999, May. Sublinear time algorithms for metric space problems. In Proceedings of the thirty-first annual ACM symposium on Theory of computing (pp. 428-434). ACM.

29 / 36

Gossip-based Truth Discovery Zhiying Xu Introduction

Motivation Motivating Examples

Problem Formulation Computational Complexity Proposed Algorithms

Exact Algorithm Approximation Algorithms

Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

Future Work

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

A Fast Algorithm for 1-median Problem

30 / 36

Gossip-based Truth Discovery Zhiying Xu Introduction

Motivation Motivating Examples

Problem Formulation Computational Complexity Proposed Algorithms

Exact Algorithm Approximation Algorithms

Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

Future Work

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Decentralized Approximation Algorithm

Implement the fast algorithm for 1-median problem. There is a trade-off between run time and accuracy.

run time: 6 log ϵ−1

1

log λ2 (W1)−1 + log2 n4 (4/σ + 1)2 σ2 log n + log ϵ−1

2

1 − λ2 (W2) 8 ln 2 + 2 ln n + ln ϵ−1 Φ W2 = I − 1 n D + P + PT n Di =

n

∑

j=1

[ Pij + Pji ] accuracy: max { 1.5 + 4ϵ1, (1 + ϵ2 + σ) f (1/15/ (1 + ϵ2 + σ)) f (1/30/ (1 + ϵ2 + σ)) }

31 / 36

Gossip-based Truth Discovery Zhiying Xu Introduction

Motivation Motivating Examples

Problem Formulation Computational Complexity Proposed Algorithms

Exact Algorithm Approximation Algorithms

Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

Future Work

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Decentralized Approximation Algorithm

32 / 36

Gossip-based Truth Discovery Zhiying Xu Introduction

Motivation Motivating Examples

Problem Formulation Computational Complexity Proposed Algorithms

Exact Algorithm Approximation Algorithms

Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

Future Work

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline

1 Introduction

Motivation Motivating Examples

2 Problem Formulation 3 Computational Complexity 4 Proposed Algorithms

Exact Algorithm Approximation Algorithms

5 Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

6 Future Work

33 / 36

Gossip-based Truth Discovery Zhiying Xu Introduction

Motivation Motivating Examples

Problem Formulation Computational Complexity Proposed Algorithms

Exact Algorithm Approximation Algorithms

Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

Future Work

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Convex Optimization of the Matrix

minimize λ2 (W ) subject to W =

n

∑

i,j=1

1 n PijWij P ≤ [0] , Pij = 0 if {i, j} / ∈ E, ∑

j

Pij = 1, ∀i. ⇒ minimize s subject to W − 11T /n ⪯ sI W =

n

∑

i,j=1

1 n PijWij P ≤ [0] , Pij = 0 if {i, j} / ∈ E, ∑

j

Pij = 1, ∀i. Semidefinite Program(SDP)

34 / 36

Gossip-based Truth Discovery Zhiying Xu Introduction

Motivation Motivating Examples

Problem Formulation Computational Complexity Proposed Algorithms

Exact Algorithm Approximation Algorithms

Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

Future Work

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline

1 Introduction

Motivation Motivating Examples

2 Problem Formulation 3 Computational Complexity 4 Proposed Algorithms

Exact Algorithm Approximation Algorithms

5 Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

6 Future Work

35 / 36

Gossip-based Truth Discovery Zhiying Xu Introduction

Motivation Motivating Examples

Problem Formulation Computational Complexity Proposed Algorithms

Exact Algorithm Approximation Algorithms

Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

Future Work

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Future Work

Simulations on real data(cooperate with Jiefeng Li) Submit to INFOCOM 2018

36 / 36

Gossip-based Truth Discovery Zhiying Xu Introduction

Motivation Motivating Examples

Problem Formulation Computational Complexity Proposed Algorithms

Exact Algorithm Approximation Algorithms

Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

Future Work

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Boyd, S., Ghosh, A., Prabhakar, B. and Shah, D., 2005, March. Gossip algorithms: Design, analysis and applications. In INFOCOM 2005. 24th Annual Joint Conference of the IEEE Computer and Communications Societies. Proceedings IEEE (Vol. 3, pp. 1653-1664). IEEE. Wang, D., Kaplan, L., Le, H. and Abdelzaher, T., 2012, April. On truth discovery in social sensing: A maximum likelihood estimation approach. In Information Processing in Sensor Networks (IPSN), 2012 ACM/IEEE 11th International Conference on (pp. 233-244). IEEE. Indyk, P., 1999, May. Sublinear time algorithms for metric space

• problems. In Proceedings of the thirty-first annual ACM

symposium on Theory of computing (pp. 428-434). ACM. Cardinal, J., Fiorini, S. and Joret, G., 2012. Minimum entropy combinatorial optimization problems. Theory of Computing Systems, 51(1), pp.4-21.

37 / 36

Gossip-based Truth Discovery Zhiying Xu Introduction

Motivation Motivating Examples

Problem Formulation Computational Complexity Proposed Algorithms

Exact Algorithm Approximation Algorithms

Decentralize and Randomize

Decentralized Algorithms Speed Up Gossip Algorithm

Future Work

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Thank You!

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