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.
翻译:在本文中,我们侧重于使用特征功能进行统计依赖性估算的问题。我们根据联合和产品边际特征功能差异的最大中心点,提出了统计依赖性计量办法。拟议计量办法可以发现两个可能不同层面的随机矢量之间的任意统计依赖性,是不同的,很容易渗透到现代机器学习和深层学习管道中。我们还用模拟数据和真实数据进行实验。我们的模拟显示,拟议方法可以测量高维、非线性数据中的统计依赖性,并且与以往的研究线上的工作相比,受维度诅咒的影响较小。对实际数据的实验表明,我们统计计量方法有可能适用于两种不同的实验推理假设情景,表明在应用监督特征提取和深度神经网络规范时,业绩特征在统计上有显著的改善。此外,我们提供了与随附的开放源库 https://bit.ly/3d4ch5I 的链接。