# Inferring the finest pattern of mutual independence from data

arXiv: https://arxiv.org/abs/2306.12984 · HTML: https://mlsanity.com/paper/2306.12984/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 51 references that are in the map.
- First posted on arXiv 22 Jun 2023.

## Builds on (most cited first, 3 of 3)

- [Kernel-based Tests for Joint Independence](https://mlsanity.com/paper/1603.00285/) (2016)
- [A Bayesian alternative to mutual information for the hierarchical clustering of dependent random variables](https://mlsanity.com/paper/1501.05194/) (2015)
- [Automated extraction of mutual independence patterns using Bayesian comparison of partition models](https://mlsanity.com/paper/2001.05407/) (2020)

## Abstract (arXiv)

For a random variable X, we are interested in the blind extraction of its finest mutual independence pattern μ ( X ). We introduce a specific kind of independence that we call dichotomic. If Delta ( X ) stands for the set of all patterns of dichotomic independence that hold for X, we show that μ ( X ) can be obtained as the intersection of all elements of Delta ( X ). We then propose a method to estimate Delta ( X ) when the data are independent and identically (i.i.d.) realizations of a multivariate normal distribution. If hatDelta ( X ) is the estimated set of valid patterns of dichotomic independence, we estimate μ ( X ) as the intersection of all patterns of hatDelta ( X ). The method is tested on simulated data, showing its advantages and limits. We also consider an application to a toy example as well as to experimental data.