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...

Directed probabilistic graphs, such as Bayesian networks, are useful tools for coherent representation of and reasoning with uncertain knowledge. They are based on the sound foundations of probability theory and they readily combine available statistics with expert judgment. When extended with decision options and measures of desirability of outcomes (utilities), they support decision making. T...

This chapter addresses strategies for selecting variables for adjustment in nonexperimental comparative effectiveness research (CER), and uses causal graphs to illustrate the causal network relating treatment to outcome. While selection approaches should be based on an understanding of the causal network representing the common cause pathways between treatment and outcome, the true causal netwo...

Structural equation models can be seen as an extension of Gaussian belief networks to cyclic graphs, and we show they can be understood generatively as the model for the joint distribution of long term average equilibrium activity of Gaussian dynamic belief networks. Most use of structural equation models in fMRI involves postulating a particular structure and comparing learnt parameters across...

Causal inference is one of the most fundamental reasoning processes and one that is essential for question-answering as well as more general AI applications such as decision-making and diagnosis. Bayesian Networks are a popular formalism for encoding (probabilistic) causal knowledge that allows for inference. We developed a system for acquiring causal knowledge from text. Our system identifies ...

In this chapter we show how algebraic geometry can be used to define and then analyse the properties of certain important classes of discrete probability models described through probability trees. Our aim is to show how much wider classes of discrete statistical models than have been considered previously have a useful algebraic formulation and unlike its competitors this class is closed under...

We introduce priors and algorithms to perform Bayesian inference in Gaussian models defined by acyclic directed mixed graphs. Such a class of graphs, composed of directed and bi-directed edges, is a representation of conditional independencies that is closed under marginalization and arises naturally from causal models which allow for unmeasured confounding. Monte Carlo methods and a variationa...