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

TL;DR

This paper explores how Mixture Density Networks can estimate continuous parameters from discrete training data, identifies bias issues, and proposes corrections to improve estimation accuracy.

Contribution

It introduces a method to use MDNs for continuous parameter estimation with discrete training data and offers bias correction techniques.

Findings

Demonstrates bias issues in MDN-based estimation from discrete data

Proposes corrective methods to reduce bias in parameter estimates

Shows improved accuracy with the proposed bias correction

Abstract

Mixture Density Networks (MDNs) can be used to generate probability density functions of model parameters $\boldsymbol{\theta}$ given a set of observables $\mathbf{x}$. In some applications, training data are available only for discrete values of a continuous parameter $\boldsymbol{\theta}$. 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.