Measuring Statistical Dependencies via Maximum Norm and Characteristic Functions
Measuring Statistical Dependencies via Maximum Norm and Characteristic Functions
复制标题
通过最大范数和特征函数测量统计依赖性
DOI：
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发表时间：
2022
期刊：
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通讯作者：
Virginijus Marcinkevičius
中科院分区：
文献类型：
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作者：
P. Daniušis;Shubham Juneja;Lukas Kuzma;Virginijus Marcinkevičius
本文主要研究利用特征函数进行统计相关估计的问题。我们提出了一个统计依赖性的措施，联合和产品边际特征函数之间的差异的最大范数的基础上。所提出的度量可以检测可能不同维度的两个随机向量之间的任意统计相关性，是可微的，并且很容易集成到现代机器学习和深度学习管道中。我们还进行了实验与模拟和真实的数据。我们的模拟表明，该方法可以测量高维非线性数据中的统计依赖性，并且与这一研究领域以前的工作相比，受维数灾难的影响较小。使用真实的数据进行的实验证明了我们的统计测量对两种不同经验推理场景的潜在适用性，当应用于监督特征提取和深度神经网络正则化时，表现出统计上显著的性能改善。此外，我们还提供了一个链接，指向随附的开源存储库https://bit.ly/3d4ch5I。
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.