# Bayesian Kernelised Test of (In)dependence with Mixed-type Variables

arXiv: https://arxiv.org/abs/2105.04001 · HTML: https://mlsanity.com/paper/2105.04001/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 24 references that are in the map.
- First posted on arXiv 9 May 2021.

## Builds on (most cited first, 4 of 4)

- [PMLB: A Large Benchmark Suite for Machine Learning Evaluation and Comparison](https://mlsanity.com/paper/1703.00512/) (2017)
- [Large-Scale Kernel Methods for Independence Testing](https://mlsanity.com/paper/1606.07892/) (2016)
- [House price estimation from visual and textual features](https://mlsanity.com/paper/1609.08399/) (2016)
- [Detecting Dependencies in Sparse, Multivariate Databases Using Probabilistic Programming and Non-parametric Bayes](https://mlsanity.com/paper/1611.01708/) (2016)

## Abstract (arXiv)

A fundamental task in AI is to assess (in)dependence between mixed-type variables (text, image, sound). We propose a Bayesian kernelised correlation test of (in)dependence using a Dirichlet process model. The new measure of (in)dependence allows us to answer some fundamental questions: Based on data, are (mixed-type) variables independent? How likely is dependence/independence to hold? How high is the probability that two mixed-type variables are more than just weakly dependent? We theoretically show the properties of the approach, as well as algorithms for fast computation with it. We empirically demonstrate the effectiveness of the proposed method by analysing its performance and by comparing it with other frequentist and Bayesian approaches on a range of datasets and tasks with mixed-type variables.