# A Statistically and Numerically Efficient Independence Test based on Random Projections and Distance Covariance

arXiv: https://arxiv.org/abs/1701.06054 · HTML: https://mlsanity.com/paper/1701.06054/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jan 2017.

## Built on by (most cited first, 4 of 4)

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- [Defending against Reconstruction Attack in Vertical Federated Learning](https://mlsanity.com/paper/2107.09898/) (2021)
- [MAPPING: Debiasing Graph Neural Networks for Fair Node Classification with Limited Sensitive Information Leakage](https://mlsanity.com/paper/2401.12824/) (2024)
- [Private measurement of nonlinear correlations between data hosted across multiple parties](https://mlsanity.com/paper/2110.09670/) (2021)

## Abstract (arXiv)

Test of independence plays a fundamental role in many statistical techniques. Among the nonparametric approaches, the distance-based methods (such as the distance correlation based hypotheses testing for independence) have numerous advantages, comparing with many other alternatives. A known limitation of the distance-based method is that its computational complexity can be high. In general, when the sample size is n, the order of computational complexity of a distance-based method, which typically requires computing of all pairwise distances, can be O(n2). Recent advances have discovered that in the it univariate cases, a fast method with O(n log n) computational complexity and O(n) memory requirement exists. In this paper, we introduces a test of independence method based on random projection and distance correlation, which achieves nearly the same power as the state-of-the-art distance-based approach, works in the it multivariate cases, and enjoys the O(n K log n) computational complexity and O(maxn,K) memory requirement, where K is the number of random projections. Note that saving is achieved when K < n/log n. We name our method a Randomly Projected Distance Covariance (RPDC). The statistical theoretical analysis takes advantage of some techniques on random projection which are rooted in contemporary machine learning. Numerical experiments demonstrate the efficiency of the proposed method, in relative to several competitors.