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

TL;DR

This paper introduces a Bayesian kernelised correlation test for mixed-type variables, enabling robust dependence assessment and probability estimation, with theoretical validation and empirical performance comparison.

Contribution

It presents a novel Bayesian kernelised dependence measure for mixed data types, with efficient algorithms and theoretical properties.

Findings

Effective in detecting dependence in mixed data

Outperforms existing methods in accuracy

Provides probabilistic dependence assessments

Abstract

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.