# Measuring Statistical Dependencies via Maximum Norm and Characteristic Functions

arXiv: https://arxiv.org/abs/2208.07934 · HTML: https://mlsanity.com/paper/2208.07934/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 38 references that are in the map.
- First posted on arXiv 16 Aug 2022.

## Builds on (most cited first, 12 of 12)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [MINE: Mutual Information Neural Estimation](https://mlsanity.com/paper/1801.04062/) (2018)
- [OpenML: networked science in machine learning](https://mlsanity.com/paper/1407.7722/) (2014)
- [The HSIC Bottleneck: Deep Learning without Back-Propagation](https://mlsanity.com/paper/1908.01580/) (2019)
- [Self-Supervised Learning with Kernel Dependence Maximization](https://mlsanity.com/paper/2106.08320/) (2021)
- [Learning Unbiased Representations via Mutual Information Backpropagation](https://mlsanity.com/paper/2003.06430/) (2020)
- [Partial Distance Correlation with Methods for Dissimilarities](https://mlsanity.com/paper/1310.2926/) (2013)
- [Measuring Dependence with Matrix-based Entropy Functional](https://mlsanity.com/paper/2101.10160/) (2021)
- [A fast algorithm for computing distance correlation](https://mlsanity.com/paper/1810.11332/) (2018)
- [From Distance Correlation to Multiscale Graph Correlation](https://mlsanity.com/paper/1710.09768/) (2017)
- [Sobolev Independence Criterion](https://mlsanity.com/paper/1910.14212/) (2019)
- [An Updated Literature Review of Distance Correlation and its Applications to Time Series](https://mlsanity.com/paper/1710.01146/) (2017)

## Built on by (most cited first, 1 of 1)

- [Testing multivariate normality by testing independence](https://mlsanity.com/paper/2311.11575/) (2023)

## Abstract (arXiv)

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.