The accurate estimation of the mutual information is a crucial task in various applications, including machine learning, communications, and biology, since it enables the understanding of complex systems. High-dimensional data render the task extremely challenging due to the amount of data to be processed and the presence of convoluted patterns. Neural estimators based on variational lower bounds of the mutual information have gained attention in recent years but they are prone to either high bias or high variance as a consequence of the partition function. We propose a novel class of discriminative mutual information estimators based on the variational representation of the $f$-divergence. We investigate the impact of the permutation function used to obtain the marginal training samples and present a novel architectural solution based on derangements. The proposed estimator is flexible as it exhibits an excellent bias/variance trade-off. Experiments on reference scenarios demonstrate that our approach outperforms state-of-the-art neural estimators both in terms of accuracy and complexity.

本文提出了一种新颖的基于 $f$-divergence 变分表示的识别互信息估计器，并在基准情景下进行的实验表明，该方法在准确性和复杂性方面优于现有的神经估计器。

基于变分$f$-散度和错排的判别式互信息估计