Distribution-Free Learning of Graphical Model Structure in Continuous Domains

Margaritis, Dimitris (2004) Distribution-Free Learning of Graphical Model Structure in Continuous Domains. Technical Report TR-ISU-CS-04-06, Computer Science, Iowa State University.

Abstract

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.