# Nonparametric independence testing via mutual information

arXiv: https://arxiv.org/abs/1711.06642 · HTML: https://mlsanity.com/paper/1711.06642/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Nov 2017.

## Built on by (most cited first, 22 of 22)

- [Rates of Estimation of Optimal Transport Maps using Plug-in Estimators via Barycentric Projections](https://mlsanity.com/paper/2107.01718/) (2021)
- [Mutual Information Estimation via Normalizing Flows](https://mlsanity.com/paper/2403.02187/) (2024)
- [Sequential Predictive Two-Sample and Independence Testing](https://mlsanity.com/paper/2305.00143/) (2023)
- [Information Bottleneck Analysis of Deep Neural Networks via Lossy Compression](https://mlsanity.com/paper/2305.08013/) (2023)
- [Exploiting Independent Instruments: Identification and Distribution Generalization](https://mlsanity.com/paper/2202.01864/) (2022)
- [A Permutation-Free Kernel Independence Test](https://mlsanity.com/paper/2212.09108/) (2022)
- [Max-Sliced Mutual Information](https://mlsanity.com/paper/2309.16200/) (2023)
- [Structure Learning for Directed Trees](https://mlsanity.com/paper/2108.08871/) (2021)
- [High-Dimensional Smoothed Entropy Estimation via Dimensionality Reduction](https://mlsanity.com/paper/2305.04712/) (2023)
- [InfoBridge: Mutual Information estimation via Bridge Matching](https://mlsanity.com/paper/2502.01383/) (2025)
- [A Simple Unified Approach to Testing High-Dimensional Conditional Independences for Categorical and Ordinal Data](https://mlsanity.com/paper/2206.04356/) (2022)
- [BEAUTY Powered BEAST](https://mlsanity.com/paper/2103.00674/) (2021)
- [Information-Theoretic Measures on Lattices for High-Order Interactions](https://mlsanity.com/paper/2408.07533/) (2024)
- [Deep Sufficient Representation Learning via Mutual Information](https://mlsanity.com/paper/2207.10772/) (2022)
- [USP: an independence test that improves on Pearson's chi-squared and the G-test](https://mlsanity.com/paper/2101.10880/) (2021)
- [Fair Clustering via Hierarchical Fair-Dirichlet Process](https://mlsanity.com/paper/2305.17557/) (2023)
- [Toward Scalable and Valid Conditional Independence Testing with Spectral Representations](https://mlsanity.com/paper/2512.19510/) (2025)
- [Functional sufficient dimension reduction through information maximization with application to classification](https://mlsanity.com/paper/2305.10880/) (2023)
- [On Ranking-based Tests of Independence](https://mlsanity.com/paper/2403.07464/) (2024)
- [A Deep Bayesian Nonparametric Framework for Robust Mutual Information Estimation](https://mlsanity.com/paper/2503.08902/) (2025)
- [Optimal structure learning and conditional independence testing](https://mlsanity.com/paper/2507.05689/) (2025)
- [When Does Context Routing Help? A Systematic Study of Multi-Modal Fusion in Time Series Forecasting](https://mlsanity.com/paper/2608.25128/) (2026)

## Abstract (arXiv)

We propose a test of independence of two multivariate random vectors, given a sample from the underlying population. Our approach, which we call MINT, is based on the estimation of mutual information, whose decomposition into joint and marginal entropies facilitates the use of recently-developed efficient entropy estimators derived from nearest neighbour distances. The proposed critical values, which may be obtained from simulation (in the case where one marginal is known) or resampling, guarantee that the test has nominal size, and we provide local power analyses, uniformly over classes of densities whose mutual information satisfies a lower bound. Our ideas may be extended to provide a new goodness-of-fit tests of normal linear models based on assessing the independence of our vector of covariates and an appropriately-defined notion of an error vector. The theory is supported by numerical studies on both simulated and real data.