We point out a limitation of the mutual information neural estimation (MINE) where the network fails to learn at the initial training phase, leading to slow convergence in the number of training iterations. To solve this problem, we propose a faster method called the mutual information neural entropic estimation (MI-NEE). Our solution first generalizes MINE to estimate the entropy using a custom reference distribution. The entropy estimate can then be used to estimate the mutual information. We argue that the seemingly redundant intermediate step of entropy estimation allows one to improve the convergence by an appropriate reference distribution. In particular, we show that MI-NEE reduces to MINE in the special case when the reference distribution is the product of marginal distributions, but faster convergence is possible by choosing the uniform distribution as the reference distribution instead. Compared to the product of marginals, the uniform distribution introduces more samples in low-density regions and fewer samples in high-density regions, which appear to lead to an overall larger gradient for faster convergence.

提出了一种更快的方法，称为互信息神经熵估计（MI-NEE），其将互信息估计变为估计熵的过程，通过使用自定义参考分布和选择均匀分布作为参考分布来实现更快的收敛。

神经熵估计：一种更快的互信息估计方法