We propose a novel approach to the problem of mutual information (MI) estimation via introducing a family of estimators based on normalizing flows. The estimator maps original data to the target distribution, for which MI is easier to estimate. We additionally explore the target distributions with known closed-form expressions for MI. Theoretical guarantees are provided to demonstrate that our approach yields MI estimates for the original data. Experiments with high-dimensional data are conducted to highlight the practical advantages of the proposed method.

翻译：我们提出了一种新颖的互信息估计方法，该方法通过引入一系列基于归一化流的估计器来解决互信息估计问题。该估计器将原始数据映射到目标分布，在此分布下互信息更易于估计。我们还探索了具有已知闭式互信息表达式的目标分布。我们提供了理论保证，以证明我们的方法能够为原始数据生成互信息估计。通过在高维数据上进行实验，我们突出了所提方法的实际优势。