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A quantification learning task estimates class ratios or class distribution given a test set. Quantification learning is useful for a variety of application domains such as commerce, public health, and politics. For instance, it is desirable to automatically estimate the proportion of customer satisfaction in different aspects from product reviews to improve customer relationships. We formulate the quantification learning problem as a maximum likelihood problem and propose the first end-to-end Deep Quantification Network (DQN) framework. DQN jointly learns quantification feature representations and directly predicts the class distribution. Compared to classification-based quantification methods, DQN avoids three separate steps: classification of individual instances, calculation of the predicted class ratios, and class ratio adjustment to account for classification errors. We evaluated DQN on four public datasets, ranging from movie and product reviews to multi-class news. We compared DQN against six existing quantification methods and conducted a sensitivity analysis of DQN performance. Compared to the best existing method in our study, (1) DQN reduces Mean Absolute Error (MAE) by about 35%. (2) DQN uses around 40% less training samples to achieve a comparable MAE.