Mixture Density Networks for Classification with an Application to
  Product Bundling
Narendhar Gugulothu Sanjay P. Bhat Tejas Bodas
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.