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

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.