Quantification, also known as class prevalence estimation, is the supervised
learning task in which a model is trained to predict the prevalence of each
class in a given bag of examples. This paper investigates the application of
deep neural networks to tasks of quantification in scenarios where it is
possible to apply a symmetric supervised approach that eliminates the need for
classification as an intermediary step, directly addressing the quantification
problem. Additionally, it discusses existing permutation-invariant layers
designed for set processing and assesses their suitability for quantification.
In light of our analysis, we propose HistNetQ, a novel neural architecture that
relies on a permutation-invariant representation based on histograms that is
specially suited for quantification problems. Our experiments carried out in
the only quantification competition held to date, show that HistNetQ
outperforms other deep neural architectures devised for set processing, as well
as the state-of-the-art quantification methods. Furthermore, HistNetQ offers
two significant advantages over traditional quantification methods: i) it does
not require the labels of the training examples but only the prevalence values
of a collection of training bags, making it applicable to new scenarios; and
ii) it is able to optimize any custom quantification-oriented loss function.

本研究探讨了深度神经网络在量化任务中的应用，并提出了适用于量化问题的基于直方图的无重排不变表示的新型神经架构 HistNetQ。通过实验结果表明，HistNetQ 在量化问题上优于其他用于集合处理的深度神经架构和现有的量化方法，具有不需要训练示例的标签但仅需要训练数据集中的流行度值的能力，并且能够优化任何自定义的量化相关损失函数。