
Asymptotic Convergence Rate of Alternating Minimization for Rank One Matrix Completion
We study alternating minimization for matrix completion in the simplest ...
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A Note on Alternating Minimization Algorithm for the Matrix Completion Problem
We consider the problem of reconstructing a low rank matrix from a subse...
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On Deterministic Sampling Patterns for Robust LowRank Matrix Completion
In this letter, we study the deterministic sampling patterns for the com...
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Lowrank Matrix Recovery from Errors and Erasures
This paper considers the recovery of a lowrank matrix from an observed ...
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Typical and Generic Ranks in Matrix Completion
We consider the problem of exact lowrank matrix completion from a geome...
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Gradient Descent for Sparse RankOne Matrix Completion for CrowdSourced Aggregation of Sparsely Interacting Workers
We consider worker skill estimation for the singlecoin DawidSkene crow...
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Matrix Completion from O(n) Samples in Linear Time
We consider the problem of reconstructing a rankk n × n matrix M from a...
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Adversarial Crowdsourcing Through Robust RankOne Matrix Completion
We consider the problem of reconstructing a rankone matrix from a revealed subset of its entries when some of the revealed entries are corrupted with perturbations that are unknown and can be arbitrarily large. It is not known which revealed entries are corrupted. We propose a new algorithm combining alternating minimization with extremevalue filtering and provide sufficient and necessary conditions to recover the original rankone matrix. In particular, we show that our proposed algorithm is optimal when the set of revealed entries is given by an ErdősRényi random graph. These results are then applied to the problem of classification from crowdsourced data under the assumption that while the majority of the workers are governed by the standard singlecoin DavidSkene model (i.e., they output the correct answer with a certain probability), some of the workers can deviate arbitrarily from this model. In particular, the "adversarial" workers could even make decisions designed to make the algorithm output an incorrect answer. Extensive experimental results show our algorithm for this problem, based on rankone matrix completion with perturbations, outperforms all other stateoftheart methods in such an adversarial scenario.
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