Distribution-Free Learning of Graphical Model Structure in Continuous Domains

TR{ISU{CS{04{06 Copyright c ° 2004 Dimitris Margaritis In this paper we present a probabilistic non-parametric conditional inde-pendence test of X and Y given a third variable Z in domains where X, Y, and Z are continuous. This test can be used for the induction of the struc-ture of a graphical model (such as a Bayesian or Markov network) from experimental data. We also provide an e®ective method for calculating it from data. We show that our method works well in practice on arti¯cial benchmark data sets constructed from a diverse set of functions. We also demonstrate learning of the structure of a graphical model in a continu-ous domain from real-world data, to our knowledge for the ¯rst time using independence-based methods and without any distributional assumptions. 1.1 Motivation and Related Work Conditional independence of X and Y given a third variable Z is de¯ned a