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.

翻译：混合密度网络(MDNs)可以用来产生模型参数的概率密度函数$\boldsymbol_theta}$$(boldsymbol_theta}$),如果有一套可观测值$\mathbf{x}$(美元)的话。在某些应用中,培训数据只能用于连续参数的离散值$\boldsymbol_theta}$(boldsymol_theta}$(美元)。在这种情况下,会出现一些可导致偏差估计的性能限制问题。我们证明在参数估计中使用MDNs,讨论偏差的起源,并为每个问题提出纠正方法。