Bayesian Networks

Abstract

Bayesian networks are today one of the most promising approaches to Data Min-ing and knowledge discovery in databases. This chapter reviews the fundamental aspects of Bayesian networks and some of their technical aspects, with a particular emphasis on the methods to induce Bayesian networks from different types of data. Basic notions are illus-trated through the detailed descriptions of two Bayesian network applications: one to survey data and one to marketing data. Born at the intersection of Artificial Intelligence, statistics and probability, Bayesian networks (Pearl, 1988) are a representation formalism at the cutting edge of knowl-edge discovery and Data Mining (Heckerman, 1997, Madigan and Ridgeway, 2003, Madigan and York, 1995). Bayesian networks belong to a more general class of mod-els called probabilistic graphical models (Whittaker, 1990,Lauritzen, 1996) that arise from the combination of graph theory and probability theory and their success rests on their ability to handle complex probabilistic models by decomposing them into smaller, amenable components. A probabilistic graphical model is defined by a graph where nodes represent stochastic variables and arcs represent dependencies among such variables. These arcs are annotated by probability distribution shaping the in-teraction between the linked variables. A probabilistic graphical model is called a Bayesian network when the graph connecting its variables is a directed acyclic graph (DAG). This graph represents conditional independence assumptions that are used to factorize the joint probability distribution of the network variables thus making the process of learning from large database amenable to computations. A Bayesian network induced from data can be used to investigate distant relationships between O. Maimon, L. Rokach (eds.), Data Mining and Knowledge Discovery Handbook, 2nd ed.,