# BEAUTY Powered BEAST

arXiv: https://arxiv.org/abs/2103.00674 · HTML: https://mlsanity.com/paper/2103.00674/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 93 references that are in the map.
- First posted on arXiv 1 Mar 2021.

## Builds on (most cited first, 21 of 21)

- [Equitability, mutual information, and the maximal information coefficient](https://mlsanity.com/paper/1301.7745/) (2013)
- [Kernel-based Tests for Joint Independence](https://mlsanity.com/paper/1603.00285/) (2016)
- [A knockoff filter for high-dimensional selective inference](https://mlsanity.com/paper/1602.03574/) (2016)
- [Nonparametric independence testing via mutual information](https://mlsanity.com/paper/1711.06642/) (2017)
- [False Discovery Rate Control via Data Splitting](https://mlsanity.com/paper/2002.08542/) (2020)
- [Hypothesis Testing For Densities and High-Dimensional Multinomials: Sharp Local Minimax Rates](https://mlsanity.com/paper/1706.10003/) (2017)
- [BET on Independence](https://mlsanity.com/paper/1610.05246/) (2016)
- [Goodness-of-fit testing in high-dimensional generalized linear models](https://mlsanity.com/paper/1908.03606/) (2019)
- [FarmTest: Factor-Adjusted Robust Multiple Testing with Approximate False Discovery Control](https://mlsanity.com/paper/1711.05386/) (2017)
- [Consistent distribution-free K-sample and independence tests for univariate random variables](https://mlsanity.com/paper/1410.6758/) (2014)
- [Multivariate tests of association based on univariate tests](https://mlsanity.com/paper/1603.03418/) (2016)
- [Optimal rates for independence testing via U-statistic permutation tests](https://mlsanity.com/paper/2001.05513/) (2020)
- [The Hellinger Correlation](https://mlsanity.com/paper/1810.10276/) (2018)
- [Flow-Based Likelihoods for Non-Gaussian Inference](https://mlsanity.com/paper/2007.05535/) (2020)
- [On Testing Independence and Goodness-of-fit in Linear Models](https://mlsanity.com/paper/1302.5831/) (2013)
- [Generalizing Distance Covariance to Measure and Test Multivariate Mutual Dependence](https://mlsanity.com/paper/1709.02532/) (2017)
- [Multiscale Fisher's Independence Test for Multivariate Dependence](https://mlsanity.com/paper/1806.06777/) (2018)
- [Testing goodness-of-fit and conditional independence with approximate co-sufficient sampling](https://mlsanity.com/paper/2007.09851/) (2020)
- [Fisher exact scanning for dependency](https://mlsanity.com/paper/1608.07885/) (2016)
- [The Binary Expansion Randomized Ensemble Test (BERET)](https://mlsanity.com/paper/1912.03662/) (2019)
- [USP: an independence test that improves on Pearson's chi-squared and the G-test](https://mlsanity.com/paper/2101.10880/) (2021)

## Built on by (most cited first, 3 of 3)

- [Data-Driven Representations for Testing Independence: Modeling, Analysis and Connection with Mutual Information Estimation](https://mlsanity.com/paper/2110.14122/) (2021)
- [BELIEF in Dependence: Leveraging Atomic Linearity in Data Bits for Rethinking Generalized Linear Models](https://mlsanity.com/paper/2210.10852/) (2022)
- [Binary Expansion Group Intersection Network](https://mlsanity.com/paper/2603.24763/) (2026)

## Abstract (arXiv)

We study distribution-free goodness-of-fit tests with the proposed Binary Expansion Approximation of UniformiTY (BEAUTY) approach. This method generalizes the renowned Euler's formula, and approximates the characteristic function of any copula through a linear combination of expectations of binary interactions from marginal binary expansions. This novel theory enables a unification of many important tests of independence via approximations from specific quadratic forms of symmetry statistics, where the deterministic weight matrix characterizes the power properties of each test. To achieve a robust power, we examine test statistics with data-adaptive weights, referred to as the Binary Expansion Adaptive Symmetry Test (BEAST). For any given alternative, we demonstrate that the Neyman-Pearson test can be approximated by an oracle weighted sum of symmetry statistics. The BEAST with this oracle provides a useful benchmark of feasible power. To approach this oracle power, we devise the BEAST through a regularized resampling approximation of the oracle test. The BEAST improves the empirical power of many existing tests against a wide spectrum of common alternatives and delivers a clear interpretation of dependency forms when significant.