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Crowdsourcing has become a popular method for collecting labeled trainingdata. However, in many practical scenarios traditional labeling can bedifficult for crowdworkers (for example, if the data is high-dimensional orunintuitive, or the labels are continuous).  In this work, we develop a novel model for crowdsourcing that can complementstandard practices by exploiting people's intuitions about groups and relationsbetween them. We employ a recent machine learning setting, called BallparkLearning, that can estimate individual labels given only coarse, aggregatedsignal over groups of data points. To address the important case of continuouslabels, we extend the Ballpark setting (which focused on classification) toregression problems. We formulate the problem as a convex optimization problemand propose fast, simple methods with an innate robustness to outliers.  We evaluate our methods on real-world datasets, demonstrating how usefulconstraints about groups can be harnessed from a crowd of non-experts. Ourmethods can rival supervised models trained on many true labels, and can obtainconsiderably better results from the crowd than a standard label-collectionprocess (for a lower price). By collecting rough guesses on groups of instancesand using machine learning to infer the individual labels, our lightweightframework is able to address core crowdsourcing challenges and train machinelearning models in a cost-effective way.

Ballpark Crowdsourcing: The Wisdom of Rough Group Comparisons