It has attracted considerable attention to use crowdsourcing services to collect a large amount of labeled data for machine learning, since crowdsourcing services allow one to ask the general public to label data at very low cost through the Internet. The use of crowdsourcing has introduced a new challenge in machine learning, that is, coping with low quality of crowd-generated data. There have been many recent attempts to address the quality problem of multiple labelers, however, there are two serious drawbacks in the existing approaches, that are, (i) non-convexity and (ii) task homogeneity. Most of the existing methods consider true labels as latent variables, which results in nonconvex optimization problems. Also, the existing models assume only single homogeneous tasks, while in realistic situations, clients can offer multiple tasks to crowds and crowd workers can work on different tasks in parallel. In this paper, we propose a convex optimization formulation of learning from crowds by introducing personal models of individual crowds without estimating true labels. We further extend the proposed model to multi-task learning based on the resemblance between the proposed formulation and that for an existing multi-task learning model. We also devise efficient iterative methods for solving the convex optimization problems by exploiting conditional independence structures in multiple classifiers.

SummaryCrowdsourcing services are often used to collect a large amount of labeled data for machine learning. Although they provide us an easy way to get labels at very low cost in a short period, they have serious limitations. One of them is the variable quality of the crowd-generated data. There have been many attempts to increase the reliability of crowdgenerated data and the quality of classifiers obtained from such data. However, in these problem settings, relatively few researchers have tried using expert-generated data to achieve further improvements. In this paper, we apply three models that deal with the problem of learning from crowds to this problem: a latent class model, a personal classifier model, and a data-dependent error model. We evaluate these methods against two baseline methods on a real data set to demonstrate the effectiveness of combining crowd-generated data and expert-generated data.

We approach the time-series forecasting problem in the presence of concept drift by automatic learning rate tuning of stochastic gradient descent (SGD). The SGD-based approach is preferable to other concept drift algorithms in that it can be applied to any model and it can keep learning efficiently whilst predicting online. Among a number of SGD algorithms, the variance-based SGD (vSGD) can successfully handle concept drift by automatic learning rate tuning, which is reduced to an adaptive mean estimation problem. However, its performance is still limited because of its heuristic mean estimator. In this paper, we present a concept-drift-aware stochastic gradient descent (Cogra), equipped with more theoretically-sound mean estimator called sequential mean tracker (SMT). Our key contribution is that we define a goodness criterion for the mean estimators; SMT is designed to be optimal according to this criterion. As a result of comprehensive experiments, we find that (i) our SMT can estimate the mean better than vSGD's estimator in the presence of concept drift, and (ii) in terms of predictive performance, Cogra reduces the predictive loss by 16-67% for real-world datasets, indicating that SMT improves the prediction accuracy significantly.

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