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Crowd Centrality

Crowd Centrality. David Karger Sewoong Oh Devavrat Shah MIT and UIUC. Crowd Sourcing. Crowd Sourcing. $30 million to land on moon. $0.05 for Image Labeling Data Entry Transcription. Micro-task Crowdsourcing. Micro-task Crowdsourcing. Left. Left.

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Crowd Centrality

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  1. Crowd Centrality David KargerSewoong Oh Devavrat Shah MIT and UIUC

  2. Crowd Sourcing

  3. Crowd Sourcing $30 million to land on moon $0.05 for Image Labeling Data Entry Transcription

  4. Micro-task Crowdsourcing

  5. Micro-task Crowdsourcing Left Left Which door is the women’s restroom? Right

  6. Micro-task Crowdsourcing Find cancerous tumor cells Reliability 90% 65% Undergrad Intern: Mturk (single label): 200 image/hr, cost: $15/hr 4000 image/hr, cost: $15/hr 90% 500 image/hr, cost: $15/hr Mturk (mult. labels):

  7. The Problem • Goal: • Reliable estimate the tasks with minimal cost • Operational questions: • Task assignment • Inferring the “answers”

  8. Task Assignment Tasks • Random ( , )-regular bipartite graphs Batches • Locally Tree-like • Sharp analysis • Good expander • High Signal to Noise Ratio

  9. Modeling The Crowd + - + - + • Binary tasks: • Worker reliability: • Necessary assumption: we know Aij

  10. Inference Problem ti • Majority: • Oracle: + - + p2 p1 p3 p4 p5

  11. Inference Problem • Majority: • Oracle: • Our Approach: p2 p1 p3 p4 p5

  12. Preview of Results Distribution of {pj}: observed to be Beta distribution by Holmes ‘10 + Ryker et al ‘10 EM algorithm : Dawid, Skene ‘79 + Sheng, Provost, Ipeirotis ‘10

  13. Preview of Results

  14. Iterative Inference • Iteratively learn • Message-passing • O(# edges) operations • Approximate MAP p2 p1 p3 p4 p5

  15. Experiments: Amazon MTurk • Learning similarities • Recommendations • Searching, …

  16. Experiments: Amazon MTurk • Learning similarities • Recommendations • Searching, …

  17. Experiments: Amazon MTurk

  18. Task Assignment: Why Random Graph

  19. Key Metric: Quality of Crowd Crowd Quality Parameter • Theorem (Karger-Oh-Shah). • Let n tasks assigned to n workers as per • an (l,l) random regular graph • Let ql > √2 • Then, for all n large enough (i.e. n =Ω(lO(log(1/q))elq))) after O(log (1/q)) iterations of the algorithm p2 p1 p3 p4 p5 • If pj = 1 for all j • q = 1 • If pj= 0.5 for all j • q =0 • q different from • μ2 = (E[2p-1])2 • q≤μ≤√q

  20. How Good Is This ? • To achieve target Perror ≤ε, we need • Per task budget l = Θ(1/q log (1/ε)) • And this is minimax optimal • Under majority voting (with any graph choice) • Per task budget required is l = Ω(1/q2 log (1/ε)) no significant gain by knowing side-information (golden question, reputation, …!)

  21. Adaptive Task Assignment: Does it Help ? • Theorem (Karger-Oh-Shah). • Given any adaptive algorithm, • let Δbe the average number of workers required per task • to achieve desired Perror ≤ε • Then there exists {pj} with quality q so that gain through adaptivity is limited

  22. Which Crowd To Employ

  23. Beyond Binary Tasks • Tasks: • Workers: • Assume pj ≥ 0.5 for all j • Let q be quality of {pj} • Results for binary task extend to this setting • Per task, number of workers required scale as • O(1/q log (1/ε) + 1/q log K) • To achieve Perror ≤ ε

  24. Beyond Binary Tasks • Converting to K-1 binary problems • each with quality ≥ q • For each x, 1 < x ≤ K: • Aij(x) = +1 if Aij≥ x, and -1 otherwise • ti(x) = +1 if ti≥ x, and -1 otherwise • Then • Corresponding quality q(x) ≥ q • Using result for binary problem, we have • Perror(x) ≤ exp(-lq/16) • Therefore • Perror ≤ Perror(2) + … + Perror(K) ≤ K exp(-lq/16)

  25. Why Algorithm Works? • MAP estimation • Prior on probability {pj} • Let f(p) be density over [0,1] • Answers A=[Aij] • Then, • Belief propagation (max-product) algorithm for MAP • With Haldane prior: pjis0 or 1 with equal probability • Iteration k+1: for all task-worker pairs (i,j) Xi/Yjrepresent log likelihood ratio for ti/pj= +1 vs-1 • This is exactly the same as our algorithm! • And our random task assignment graph is tree-like • That is, our algorithm is effectively MAP for Haldane prior

  26. Why Algorithm Works? • A minor variation of this algorithm • Tinext = Tijnext= ΣWij’ Aij’ = ΣWj’ Aij’ • Wjnext= Wijnext= ΣTi’jAi’j = ΣTi’ Ai’j • Then, • Tnext= AAT T • (subject to this modification) our algorithm is computing • Left signular vector of A (corresponding to largest s.v.) • So why compute rank-1 approximation of A ?

  27. Why Algorithm Works? • Random graph + probabilistic model • E[Aij] = (tipj- (1-pj)ti) l/n =ti(2pj-1)l/n • E[A] = t (2p-1)T l/n • That is, • E[A] is rank-1 matrix • And, t is the left singular vector of E[A] • If A ≈ E[A] • Then computing left singular vector of A makes sense • Building upon Friedman-Kahn-Szemeredi ‘89 • Singular vector of A provides reasonable approximation • Perror = O(1/lq) • Ghosh, Kale, Mcafee’12 • For sharper result we use belief propagation

  28. Concluding Remarks • Budget optimal micro-task crowd sourcing via • Random regular task allocation graph • Belief propagation • Key messages • All that matters is quality of crowd • Worker reputation is not useful for non-adaptive tasks • Adaptation does not help due to fleeting nature of workers • Reputation + worker id needed for adaptation to be effective • Inference algorithm can be useful for assigning reputation • Model of binary task is equivalent to K-ary tasks

  29. On That Note…

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