# Mixture Density Network Estimation of Continuous Variable Maximum Likelihood Using Discrete Training Samples

arXiv: https://arxiv.org/abs/2103.13416 · HTML: https://mlsanity.com/paper/2103.13416/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 13 references that are in the map.
- First posted on arXiv 24 Mar 2021.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [A Guide to Constraining Effective Field Theories with Machine Learning](https://mlsanity.com/paper/1805.00020/) (2018)
- [Parameter Estimation using Neural Networks in the Presence of Detector Effects](https://mlsanity.com/paper/2010.03569/) (2020)

## Abstract (arXiv)

Mixture Density Networks (MDNs) can be used to generate probability density functions of model parameters boldsymbolθ given a set of observables x. In some applications, training data are available only for discrete values of a continuous parameter boldsymbolθ. In such situations a number of performance-limiting issues arise which can result in biased estimates. We demonstrate the usage of MDNs for parameter estimation, discuss the origins of the biases, and propose a corrective method for each issue.