While mixture density networks (MDNs) have been extensively used for
regression tasks, they have not been used much for classification tasks. One
reason for this is that the usability of MDNs for classification is not clear
and straightforward. In this paper, we propose two MDN-based models for
classification tasks. Both models fit mixtures of Gaussians to the the data and
use the fitted distributions to classify a given sample by evaluating the
learnt cumulative distribution function for the given input features. While the
proposed MDN-based models perform slightly better than, or on par with, five
baseline classification models on three publicly available datasets, the real
utility of our models comes out through a real-world product bundling
application. Specifically, we use our MDN-based models to learn the
willingness-to-pay (WTP) distributions for two products from synthetic sales
data of the individual products. The Gaussian mixture representation of the
learnt WTP distributions is then exploited to obtain the WTP distribution of
the bundle consisting of both the products. The proposed MDN-based models are
able to approximate the true WTP distributions of both products and the bundle
well.

本文提出了两种基于混合密度网络的分类模型，通过将高斯混合模型拟合到数据中，并使用拟合的分布通过评估学习到的累积分布函数对给定样本进行分类。这些模型在三个公开数据集上表现略优于或与五个基准分类模型相当，并通过真实世界的产品捆绑应用展示了其实际用途。具体而言，我们使用这些模型从单个产品的合成销售数据中学习愿意支付（WTP）分布，并利用所学到的 WTP 分布的高斯混合表示来获得由两个产品组成的捆绑产品的 WTP 分布。这些提出的基于混合密度网络的模型能够很好地近似两个产品和捆绑产品的真实 WTP 分布。