Quantification is the machine learning task of estimating test-data class proportions that are not necessarily similar to those in training. Apart from its intrinsic value as an aggregate statistic, quantification output can also be used to optimize classifier probabilities, thereby increasing classification accuracy. We unify major quantification approaches under a constrained multi-variate regression framework, and use mathematical programming to estimate class proportions for different loss functions. With this modeling approach, we extend existing binary-only quantification approaches to multi-class settings as well. We empirically verify our unified framework by experimenting with several multi-class datasets including the Stanford Sentiment Treebank and CIFAR-10.
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