Gradient Descent for Sparse RankOne Matrix Completion for CrowdSourced Aggregation of Sparsely Interacting Workers
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Proceedings of the 35th International Conference on Machine Learning, PMLR 80:33353344, 2018.
Abstract
We consider worker skill estimation for the single coin DawidSkene crowdsourcing model. In practice skillestimation is challenging because worker assignments are sparse and irregular due to the arbitrary, and uncontrolled availability of workers. We formulate skill estimation as a rankone correlationmatrix completion problem, where the observed components correspond to observed label correlation between workers. We show that the correlation matrix can be successfully recovered and skills identifiable if and only if the sampling matrix (observed components) is irreducible and aperiodic. We then propose an efficient gradient descent scheme and show that skill estimates converges to the desired global optima for such sampling matrices. Our proof is original and the results are surprising in light of the fact that even the weighted rankone matrix factorization problem is NP hard in general. Next we derive sample complexity bounds for the noisy case in terms of spectral properties of the signless Laplacian of the sampling matrix. Our proposed scheme achieves stateofart performance on a number of realworld datasets.
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