In this paper, we focus on the problem of statistical dependence estimation using characteristic functions. We propose a statistical dependence measure, based on the maximum-norm of the difference between joint and product-marginal characteristic functions. The proposed measure can detect arbitrary statistical dependence between two random vectors of possibly different dimensions, is differentiable, and easily integrable into modern machine learning and deep learning pipelines. We also conduct experiments both with simulated and real data. Our simulations show, that the proposed method can measure statistical dependencies in high-dimensional, non-linear data, and is less affected by the curse of dimensionality, compared to the previous work in this line of research. The experiments with real data demonstrate the potential applicability of our statistical measure for two different empirical inference scenarios, showing statistically significant improvement in the performance characteristics when applied for supervised feature extraction and deep neural network regularization. In addition, we provide a link to the accompanying open-source repository https://bit.ly/3d4ch5I.

本文提出了一种基于最大范数的统计依赖测量方法，旨在探究两个可能具有不同维度的随机向量间任意统计依赖的检测，该方法具有可微性并易于集成现代机器学习和深度学习管道，实验表明该方法比先前工作在高维和非线性数据中测量统计依赖的应对困难性低，此外，我们提供了该开放源代码存储库的链接。

通过最大范和特征函数测量统计依赖