Causation, Prediction, and Search

Abstract

To Martha, for her support and loveR .S. One source of the ideas in this book is in work we began ten years ago at the University of Pittsburgh. We drew many ideas about causality, statistics and search from the psychometric, economic and sociological literature, beginning with Charles Spearman's project at the turn of the century and including the work of Herbert Simon, Hubert Blalock and Herbert Costner. We obtained a new perspective on the enterprise from Judea Pearl's Probabilistic Reasoning in Intelligent Systems, which appeared the next year. Although not principally concerned with discovery, Pearl's book showed us how to connect conditional independence with causal structure quite generally, and that connection proved essential to establishing general, reliable discovery procedures. We have since profited from correspondence and conversation with Pearl and with Dan Geiger and Thomas Verma, and from several of their papers. Pearl's work drew on the papers of Wermuth (1980), Kiiveri and Speed (1982), Wermuth and Lauritzen (1983), and Kiiveri, Speed and Carlin (1984), which in the early 1980s had already provided the foundations for a rigorous study of causal inference. Paul Holland introduced one of us to the Rubin framework some years ago, but we only recently realized it's logical connections with directed graphical models. We were further helped by J. Whittaker's (1990) excellent account of the properties of undirected graphical models. We have learned a great deal from Gregory Cooper at the University of Pittsburgh who provided us with data, comments, Bayesian algorithms and the picture and description of the ALARM network which we consider in several places. Over the years we have learned useful things from Kenneth Bollen. Chris Meek provided essential help in obtaining an important theorem that derives various claims made by Rubin, Pratt and Schlaifer from axioms on directed graphical models. Steve Fienberg and several students from Carnegie Mellon's department of statistics joined with us in a seminar on graphical models from which we learned a great deal. We are indebted to him for his openness, intelligence and helpfulness in our research, and to Elizabeth Slate for guiding us through several papers in the Rubin framework. We are obliged to Nancy Cartwright for her courteous but salient criticism of the approach taken in our previous book and continued here. Her comments prompted our work on parameters in Causation, Prediction, and Search Chapter 4. We are indebted to Brian Skyrms for his interest and encouragement over many years, and to Marek Druzdzel for helpful comments and encouragement. We have also been

The Advantage of Timely Intervention.

“…In the first two experiments, the model was semideterministic such that a cause could occur without its effect (e.g., P[P͉E] Ͻ 1) but an effect could not occur without its cause (e.g., P[P͉ϳE] ϭ 0). One feature of such a semideterministic chain model is that it cannot be learned by constraint-based algorithms (e.g., TETRAD; see Spirtes et al, 1993) that infer graph structure from the determination of pairwise unconditional and conditional dependencies. This is because such an algorithm needs to compute all the relevant conditional independencies in the generated data, but some of these will be undefined when the learning set is semideterministic.…”

“…A formal framework for causal inference based on causal Bayes networks has been recently developed (Pearl, 2000;Spirtes, Glymour, & Schienes, 1993). This approach clarifies the relation between the probabilistic dependencies present in a set of data and the causal models that could have generated that data.…”

“…There are two main approaches in the literature here: bottom-up constraint-based methods (e.g., Spirtes et al, 1993) and top-down Bayesian methods (e.g., Heckerman, Meek, & Cooper, 1999). Applied to human causal induction, the bottom-up approach supposes that people encode information about the probabilistic dependencies present in the experienced data and use this information to generate Markov equivalent causal models.…”

“…It represents the intuition that if one intervenes to stop the current flow, one cannot draw any new conclusions about the status of the battery. 2 One can, however, expect the light to go off, because the causal link from current flow to light remains intact (for full details see Pearl, 2000;Spirtes, Glymour, & Schienes, 1993).…”

“…Models that share the same conditional and unconditional dependencies are termed Markov equivalent (Pearl, 2000;Spirtes et al, 1993). An appropriate intervention, however, enables the two structures to be distinguished.…”