We propose a streaming algorithm for the binary classification of data based on crowdsourcing. The algorithm learns the competence of each labeller by comparing her labels to those of other labellers on the same tasks and uses this information to minimize the prediction error rate on each task. We provide performance guarantees of our algorithm for a fixed population of independent labellers. In particular, we show that our algorithm is optimal in the sense that the cumulative regret compared to the optimal decision with known labeller error probabilities is finite, independently of the number of tasks to label. The complexity of the algorithm is linear in the number of labellers and the number of tasks, up to some logarithmic factors. Numerical experiments illustrate the performance of our algorithm compared to existing algorithms, including simple majority voting and expectation-maximization algorithms, on both synthetic and real datasets.
Crowdsourcing has become a popular paradigm for labeling large datasets. However, it has given rise to the computational task of aggregating the crowdsourced labels provided by a collection of unreliable annotators. We approach this problem by transforming it into a standard inference problem in graphical models, and applying approximate variational methods, including belief propagation (BP) and mean field (MF). We show that our BP algorithm generalizes both majority voting and a recent algorithm by [1], while our MF method is closely related to a commonly used EM algorithm. In both cases, we find that the performance of the algorithms critically depends on the choice of a prior distribution on the workers' reliability; by choosing the prior properly, both BP and MF (and EM) perform surprisingly well on both simulated and real-world datasets, competitive with state-of-the-art algorithms based on more complicated modeling assumptions. In this paper we analyze a crowdsourcing system consisting of a set of users and a set of binary choice questions. Each user has an unknown, fixed, reliability that determines the user's error rate in answering questions. The problem is to determine the truth values of the questions solely based on the user answers. Although this problem has been studied extensively, theoretical error bounds have been shown only for restricted settings: when the graph between users and questions is either random or complete. In this paper we consider a general setting of the problem where the user--question graph can be arbitrary. We obtain bounds on the error rate of our algorithm and show it is governed by the expansion of the graph. We demonstrate, using several synthetic and real datasets, that our algorithm outperforms the state of the art. A large fraction of user-generated content on the Web, such as posts or comments on popular online forums, consists of abuse or spam. Due to the volume of contributions on popular sites, a few trusted moderators cannot identify all such abusive content, so viewer ratings of contributions must be used for moderation. But not all viewers who rate content are trustworthy and accurate. What is a principled approach to assigning trust and aggregating user ratings, in order to accurately identify abusive content? In this paper, we introduce a framework to address the problem of moderating online content using crowdsourced ratings. Our framework encompasses users who are untrustworthy or inaccurate to an unknown extent --- that is, both the content and the raters are of unknown quality. With no knowledge whatsoever about the raters, it is impossible to do better than a random estimate. We present efficient algorithms to accurately detect abuse that only require knowledge about the identity of a single 'good' agent, who rates contributions accurately more than half the time. We prove that our algorithm can infer the quality of contributions with error that rapidly converges to zero as the number of observations increases; we also numerically demonstrate that the algorithm has very high accuracy for much fewer observations. Finally, we analyze the robustness of our algorithms to manipulation by adversarial or strategic raters, an important issue in moderating online content, and quantify how the performance of the algorithm degrades with the number of manipulating agents. For many supervised learning tasks it may be infeasible (or very expensive) to obtain objective and reliable labels. Instead, we can collect subjective (possibly noisy) labels from multiple experts or annotators. In practice, there is a substantial amount of disagreement among the annotators, and hence it is of great practical interest to address conventional supervised learning problems in this scenario. In this paper we describe a probabilistic approach for supervised learning when we have multiple annotators providing (possibly noisy) labels but no absolute gold standard. The proposed algorithm evaluates the different experts and also gives an estimate of the actual hidden labels. Experimental results indicate that the proposed method is superior to the commonly used majority voting baseline. Crowdsourcing systems, in which numerous tasks are electronically distributed to numerous “information pieceworkers,” have emerged as an effective paradigm for human-powered solving of large-scale problems in domains such as image classification, data entry, optical character recognition, recommendation, and proofreading. Because these low-paid workers can be unreliable, nearly all such systems must devise schemes to increase confidence in their answers, typically by assigning each task multiple times and combining the answers in an appropriate manner, e.g., majority voting. In this paper, we consider a general model of such crowdsourcing tasks and pose the problem of minimizing the total price i.e., number of task assignments that must be paid to achieve a target overall reliability. We give a new algorithm for deciding which tasks to assign to which workers and for inferring correct answers from the workers' answers. We show that our algorithm, inspired by belief propagation and low-rank matrix approximation, significantly outperforms majority voting and, in fact, is optimal through comparison to an oracle that knows the reliability of every worker. Further, we compare our approach with a more general class of algorithms that can dynamically assign tasks. By adaptively deciding which questions to ask to the next set of arriving workers, one might hope to reduce uncertainty more efficiently. We show that, perhaps surprisingly, the minimum price necessary to achieve a target reliability scales in the same manner under both adaptive and nonadaptive scenarios. Hence, our nonadaptive approach is order optimal under both scenarios. This strongly relies on the fact that workers are fleeting and cannot be exploited. Therefore, architecturally, our results suggest that building a reliable worker-reputation system is essential to fully harnessing the potential of adaptive designs. Crowdsourcing systems, in which tasks are electronically distributed to numerous "information piece-workers", have emerged as an effective paradigm for human-powered solving of large scale problems in domains such as image classification, data entry, optical character recognition, recommendation, and proofreading. Because these low-paid workers can be unreliable, nearly all crowdsourcers must devise schemes to increase confidence in their answers, typically by assigning each task multiple times and combining the answers in some way such as majority voting. In this paper, we consider a general model of such crowdsourcing tasks, and pose the problem of minimizing the total price (i.e., number of task assignments) that must be paid to achieve a target overall reliability. We give a new algorithm for deciding which tasks to assign to which workers and for inferring correct answers from the workers' answers. We show that our algorithm significantly outperforms majority voting and, in fact, is asymptotically optimal through comparison to an oracle that knows the reliability of every worker.  Labeling large datasets has become faster, cheaper, and easier with the advent of crowdsourcing services like Amazon Mechanical Turk. How can one trust the labels obtained from such services? We propose a model of the labeling process which includes label uncertainty, as well a multi-dimensional measure of the annotators' ability. From the model we derive an online algorithm that estimates the most likely value of the labels and the annotator abilities. It finds and prioritizes experts when requesting labels, and actively excludes unreliable annotators. Based on labels already obtained, it dynamically chooses which images will be labeled next, and how many labels to request in order to achieve a desired level of confidence. Our algorithm is general and can handle binary, multi-valued, and continuous annotations (e.g. bounding boxes). Experiments on a dataset containing more than 50,000 labels show that our algorithm reduces the number of labels required, and thus the total cost of labeling, by a large factor while keeping error rates low on a variety of datasets.