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We consider worker skill estimation for the single-coin Dawid-Skenecrowdsourcing model. In practice, skill-estimation is challenging becauseworker assignments are sparse and irregular due to the arbitrary anduncontrolled availability of workers. We formulate skill estimation as arank-one correlation-matrix completion problem, where the observed componentscorrespond to observed label correlations between workers. We show that thecorrelation matrix can be successfully recovered and skills are identifiable ifand only if the sampling matrix (observed components) does not have a bipartiteconnected component. We then propose a projected gradient descent scheme andshow that skill estimates converge to the desired global optima for suchsampling matrices. Our proof is original and the results are surprising inlight of the fact that even the weighted rank-one matrix factorization problemis NP-hard in general. Next, we derive sample complexity bounds in terms ofspectral properties of the signless Laplacian of the sampling matrix. Ourproposed scheme achieves state-of-art performance on a number of real-worlddatasets.

Gradient Descent for Sparse Rank-One Matrix Completion for Crowd-Sourced Aggregation of Sparsely Interacting Workers