A companion set of lecture slides is available at

Bayesian networks are normally given one of two types of foundations: they are either treated purely formally as an abstract way of representing probability functions, or they are interpreted, with some causal interpretation given to the graph in a network and some standard interpretation of probability given to the probabilities specified in the network. In this chapter I argue that current foundations are problematic, and put forward new foundations which involve aspects of both the interpreted and the formal approaches. One standard approach is to interpret a Bayesian network objectively: the graph in a Bayesian network represents causality in the world and the specified probabilities are objective, empirical probabilities. Such an interpretation founders when the Bayesian network independence assumption (often called the causal Markov condition) fails to hold. In §2 I catalogue the occasions when the independence assumption fails, and show that such failures are pervasive. Next, in §3, I show that even where the independence assumption does hold objectively, an agent’s causal knowledge is unlikely to satisfy the assumption with respect to her subjective probabilities, and that slight differences between an agent’s subjective Bayesian network and an objective Bayesian network can lead to large differences between probability distributions determined by these networks. To overcome these difficulties I put forward logical Bayesian foundations in §5. I show that if the graph and probability specification in a Bayesian network are thought of as an agent’s background knowledge, then the agent is most rational if she adopts the probability distribution determined by the

presented at

Abstract not found

. Association rules discovered through attribute-oriented induction are commonly used in data mining tools to express relationships between variables. However, causal inference algorithms discover more concise relationships between variables, namely, relations of direct cause . These algorithms produce regressive structured equation models for continuous linear data and Bayes networks for discrete data. This work compares the effectiveness of causal inference algorithms with association rule induction for discovering patterns in discrete data. 1 Introduction Association rules discovered using attribute-oriented induction in tools such as DBMiner are used to express relationships among variables. However, causal inference algorithms discover deeper relationships, namely a variety of causal relationships including genuine causality, potential causality and spurious association [7,8]. In this paper, we describe and compare association rule generation based on their implementation...

Abstract not found