Efficient crowdsourcing for multi-class labeling

Crowdsourcing systems like Amazon's Mechanical Turk have emerged as an effective large-scale human-powered platform for performing tasks in domains such as image classification, data entry, recommendation, and proofreading. Since workers are low-paid (a few cents per task) and tasks performed are monotonous, the answers obtained are noisy and hence unreliable. To obtain reliable estimates, it is essential to utilize appropriate inference algorithms (e.g. Majority voting) coupled with structured redundancy through task assignment. Our goal is to obtain the best possible trade-off between reliability and redundancy. In this paper, we consider a general probabilistic model for noisy observations for crowd-sourcing systems and pose the problem of minimizing the total price (i.e. redundancy) that must be paid to achieve a target overall reliability. Concretely, we show that it is possible to obtain an answer to each task correctly with probability 1-ε as long as the redundancy per task is O((K/q) log (K/ε)), where each task can have any of the $K$ distinct answers equally likely, q is the crowd-quality parameter that is defined through a probabilistic model. Further, effectively this is the best possible redundancy-accuracy trade-off any system design can achieve. Such a single-parameter crisp characterization of the (order-)optimal trade-off between redundancy and reliability has various useful operational consequences. Further, we analyze the robustness of our approach in the presence of adversarial workers and provide a bound on their influence on the redundancy-accuracy trade-off. Unlike recent prior work [GKM11, KOS11, KOS11], our result applies to non-binary (i.e. K>2) tasks. In effect, we utilize algorithms for binary tasks (with inhomogeneous error model unlike that in [GKM11, KOS11, KOS11]) as key subroutine to obtain answers for K-ary tasks. Technically, the algorithm is based on low-rank approximation of weighted adjacency matrix for a random regular bipartite graph, weighted according to the answers provided by the workers.National Science Foundation (U.S.

Gradient descent for sparse rank-one matrix completion for crowd-sourced aggregation of sparsely interacting workers

We consider worker skill estimation for the singlecoin Dawid-Skene crowdsourcing model. In practice skill-estimation is challenging because worker assignments are sparse and irregular due to the arbitrary, and uncontrolled availability of workers. We formulate skill estimation as a rank-one correlation-matrix 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 rank-one 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 state-of-art performance on a number of real-world datasets.Published versio

Crowdsourcing with Sparsely Interacting Workers

We consider estimation of worker skills from worker-task interaction data (with unknown labels) for the single-coin crowd-sourcing binary classification model in symmetric noise. We define the (worker) interaction graph whose nodes are workers and an edge between two nodes indicates whether or not the two workers participated in a common task. We show that skills are asymptotically identifiable if and only if an appropriate limiting version of the interaction graph is irreducible and has odd-cycles. We then formulate a weighted rank-one optimization problem to estimate skills based on observations on an irreducible, aperiodic interaction graph. We propose a gradient descent scheme and show that for such interaction graphs estimates converge asymptotically to the global minimum. We characterize noise robustness of the gradient scheme in terms of spectral properties of signless Laplacians of the interaction graph. We then demonstrate that a plug-in estimator based on the estimated skills achieves state-of-art performance on a number of real-world datasets. Our results have implications for rank-one matrix completion problem in that gradient descent can provably recover $W \times W$ rank-one matrices based on $W+1$ off-diagonal observations of a connected graph with a single odd-cycle

Optimal Inference in Crowdsourced Classification via Belief Propagation

Crowdsourcing systems are popular for solving large-scale labelling tasks with low-paid workers. We study the problem of recovering the true labels from the possibly erroneous crowdsourced labels under the popular Dawid-Skene model. To address this inference problem, several algorithms have recently been proposed, but the best known guarantee is still significantly larger than the fundamental limit. We close this gap by introducing a tighter lower bound on the fundamental limit and proving that Belief Propagation (BP) exactly matches this lower bound. The guaranteed optimality of BP is the strongest in the sense that it is information-theoretically impossible for any other algorithm to correctly label a larger fraction of the tasks. Experimental results suggest that BP is close to optimal for all regimes considered and improves upon competing state-of-the-art algorithms.Comment: This article is partially based on preliminary results published in the proceeding of the 33rd International Conference on Machine Learning (ICML 2016