Big Data promises to advance science through data-driven discovery. However, many standard lab protocols rely on manual examination, which is not feasible for large-scale datasets. Meanwhile, automated approaches lack the accuracy of expert examination. We propose to 1) start with expertly labeled data, 2) amplify labels through web applications that engage citizen scientists, and 3) train machine learning on amplified labels, to emulate the experts. Demonstrating this, we developed a system to quality control brain magnetic resonance images. Expert-labeled data were amplified by citizen scientists through a simple web interface. A deep learning algorithm was then trained to predict data quality, based on citizen scientist labels. Deep learning performed as well as specialized algorithms for quality control (AUC=0.99). Combining citizen science and deep learning can generalize and scale expert decision making; this is particularly important in disciplines where specialized, automated tools do not yet exist.