A Bayesian Multiresolution Independence Test for Continuous Variables

TL;DR

This paper introduces a Bayesian multiresolution independence test for continuous variables, enabling more accurate detection of independence by analyzing data at multiple resolutions using exact posterior probability computations.

Contribution

It presents a novel Bayesian approach that computes the posterior probability of independence across various resolutions, improving reliability over single-resolution methods.

Findings

Effective at detecting independence in continuous data

Applicable to Bayesian network structure learning

Handles mixed variable types seamlessly

Abstract

In this paper we present a method ofcomputing the posterior probability ofconditional independence of two or morecontinuous variables from data,examined at several resolutions. Ourapproach is motivated by theobservation that the appearance ofcontinuous data varies widely atvarious resolutions, producing verydifferent independence estimatesbetween the variablesinvolved. Therefore, it is difficultto ascertain independence withoutexamining data at several carefullyselected resolutions. In our paper, weaccomplish this using the exactcomputation of the posteriorprobability of independence, calculatedanalytically given a resolution. Ateach examined resolution, we assume amultinomial distribution with Dirichletpriors for the discretized tableparameters, and compute the posteriorusing Bayesian integration. Acrossresolutions, we use a search procedureto approximate the Bayesian integral ofprobability over an exponential numberof possible histograms. Our methodgeneralizes to an arbitrary numbervariables in a straightforward manner.The test is suitable for Bayesiannetwork learning algorithms that useindependence tests to infer the networkstructure, in domains that contain anymix of continuous, ordinal andcategorical variables.