# Data-Driven Representations for Testing Independence: Modeling, Analysis and Connection with Mutual Information Estimation

arXiv: https://arxiv.org/abs/2110.14122 · HTML: https://mlsanity.com/paper/2110.14122/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 53 references that are in the map.
- First posted on arXiv 27 Oct 2021.

## Builds on (most cited first, 9 of 9)

- [Conditional independence testing based on a nearest-neighbor estimator of conditional mutual information](https://mlsanity.com/paper/1709.01447/) (2017)
- [Model-Powered Conditional Independence Test](https://mlsanity.com/paper/1709.06138/) (2017)
- [Kernel-based Tests for Joint Independence](https://mlsanity.com/paper/1603.00285/) (2016)
- [Conditional Independence Testing using Generative Adversarial Networks](https://mlsanity.com/paper/1907.04068/) (2019)
- [BET on Independence](https://mlsanity.com/paper/1610.05246/) (2016)
- [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)
- [BEAUTY Powered BEAST](https://mlsanity.com/paper/2103.00674/) (2021)
- [Fisher exact scanning for dependency](https://mlsanity.com/paper/1608.07885/) (2016)

## Built on by (most cited first, 2 of 2)

- [Fault Detection and Monitoring using a Data-Driven Information-Based Strategy: Method, Theory, and Application](https://mlsanity.com/paper/2405.03667/) (2024)
- [On Ranking-based Tests of Independence](https://mlsanity.com/paper/2403.07464/) (2024)

## Abstract (arXiv)

This work addresses testing the independence of two continuous and finite-dimensional random variables from the design of a data-driven partition. The empirical log-likelihood statistic is adopted to approximate the sufficient statistics of an oracle test against independence (that knows the two hypotheses). It is shown that approximating the sufficient statistics of the oracle test offers a learning criterion for designing a data-driven partition that connects with the problem of mutual information estimation. Applying these ideas in the context of a data-dependent tree-structured partition (TSP), we derive conditions on the TSP's parameters to achieve a strongly consistent distribution-free test of independence over the family of probabilities equipped with a density. Complementing this result, we present finite-length results that show our TSP scheme's capacity to detect the scenario of independence structurally with the data-driven partition as well as new sampling complexity bounds for this detection. Finally, some experimental analyses provide evidence regarding our scheme's advantage for testing independence compared with some strategies that do not use data-driven representations.