Distribution-Free Learning of Graphical Model Structure in Continuous Domains
Dimitris Margaritis · Iowa State University Digital Repository (Iowa State University) · 2004
In this paper we present a probabilistic non-parametric conditional independence 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 structure of a graphical model (such as a Bayesian or Markov network) from experimental data. We also provide an effective method for calculating it from data. We show that our method works well in practice on artificial benchmark data sets constructed from a diverse set of functions. We also demonstrate learning of the structure of a graphical model in a continuous domain from real-world data, to our knowledge for the first 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 defined as independence of X and Y for every value z of Z almost surely i.e., except a subset of zero probability (Lauritzen, 1996). In this paper we address the problem of testing for conditional independence when the variables X, Y, and Z are continuous. Such a test can be used as a key building block