A Bayesian Multiresolution Independence Test for Continuous Variables
Dimitris Margaritis, Sebastian Thrun
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.
PDF Link: /papers/01/p346-margaritis.pdf
AUTHOR = "Dimitris Margaritis
and Sebastian Thrun",
TITLE = "A Bayesian Multiresolution Independence Test for Continuous Variables",
BOOKTITLE = "Proceedings of the Seventeenth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-01)",
PUBLISHER = "Morgan Kaufmann",
ADDRESS = "San Francisco, CA",
YEAR = "2001",
PAGES = "346--353"