# Mixture Density Networks for Classification with an Application to Product Bundling

arXiv: https://arxiv.org/abs/2402.05428 · HTML: https://mlsanity.com/paper/2402.05428/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 26 references that are in the map.
- First posted on arXiv 8 Feb 2024.

## Builds on (most cited first, 4 of 4)

- [Continuous 3D Multi-Channel Sign Language Production via Progressive Transformers and Mixture Density Networks](https://mlsanity.com/paper/2103.06982/) (2021)
- [Graph Mixture Density Networks](https://mlsanity.com/paper/2012.03085/) (2020)
- [Quantifying Multimodality in World Models](https://mlsanity.com/paper/2112.07263/) (2021)
- [Unsupervised Learning for Surgical Motion by Learning to Predict the Future](https://mlsanity.com/paper/1806.03318/) (2018)

## Built on by (most cited first, 2 of 2)

- [LLM-Prior: A Framework for Knowledge-Driven Prior Elicitation and Aggregation](https://mlsanity.com/paper/2508.03766/) (2025)
- [Benchmarking machine learning models for multi-class state recognition in double quantum dot data](https://mlsanity.com/paper/2511.22451/) (2025)

## Abstract (arXiv)

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.