This paper concerns the empirical basis of causation, and addresses the following issues: 1. the clues that might prompt people to perceive causal relationships in uncontrolled observations. 2. the task of inferring causal models from these clues, and 3. whether the models inferred tell us anything useful about the causal mechanisms that underly the observations. We propose a minimal-model semantics of causation, and show that, contrary to common folklore, genuine causal influences can be distinguished from spurious covariations following standard norms of inductive reasoning. We also establish a sound characterization of the conditions under which such a distinction is possible. We provide an effective algorithm for inferred causation and show that, for a large class of data the algorithm can uncover the direction of causal influences as defined above. Finally, we address the issue of non-temporal causation. 1 Introduction The study of causation is central to the understanding of hum...

The authors outline a cognitive and computational account of causal learning in children. They propose that children use specialized cognitive systems that allow them to recover an accurate “causal map ” of the world: an abstract, coherent, learned representation of the causal relations among events. This kind of knowledge can be perspicuously understood in terms of the formalism of directed graphical causal models, or Bayes nets. Children’s causal learning and inference may involve computations similar to those for learning causal Bayes nets and for predicting with them. Experimental results suggest that 2to 4-year-old children construct new causal maps and that their learning is consistent with the Bayes net formalism.

This paper develops axioms and formal semantics for statements of the form "X is causally irrelevant to Y in context Z," which we interpret to mean "Changing X will not affect Y if we hold Z constant." The axiomization of causal irrelevance is contrasted with the axiomization of informational irrelevance, as in "Learning X will not alter our belief in Y , once we know Z." Two versions of causal irrelevance are analyzed, probabilistic and deterministic. We show that, unless stability is assumed, the probabilistic definition yields a very loose structure, that is governed by just two trivial axioms. Under the stability assumption, probabilistic causal irrelevance is isomorphic to path interception in cyclic graphs. Under the deterministic definition, causal irrelevance complies with all of the axioms of path interception in cyclic graphs, with the exception of transitivity. We compare our formalism to that of [Lewis, 1973], and offer a graphical method of proving theorems abou...

The direct effect of one event on another can be defined and measured by holding constant all intermediate variables between the two. Indirect effects present conceptual and practical difficulties (in nonlinear models), because they cannot be isolated by holding certain variables constant. This paper presents a new way of defining the effect transmitted through a restricted set of paths, without controlling variables on the remaining paths. This permits the assessment of a more natural type of direct and indirect effects, one that is applicable in both linear and nonlinear models and that has broader policy-related interpretations. The paper establishes conditions under which such assessments can be estimated consistently from experimental and nonexperimental data, and thus extends path-analytic techniques to nonlinear and nonparametric models.

This paper summarizes basic concepts and principles that I have found to be useful in dealing with causal reasoning. The paper is written as a companion to a lecture under the same title, to be presented at IJCAI-99, and is intended to supplement the lecture with technical details and pointers to more elaborate discussions in the literature. The ruling conception will be to treat causation as a computational schema devised to identify the invariant relationships in the environment, so as to facilitate reliable prediction of the effect of actions. This conception, as well as several of its satellite principles and tools, has been guiding paradigm for several research communities in AI, most notably those connected with causal discovery, troubleshooting, planning under uncertainty and modeling the behavior of physical systems. My hopes are to encourage a broader and more effective usage of causal modeling by explicating these common principles in simple and familiar mathematical form. Af...

This paper builds on the structural equations, treatment effect, and machine learning literatures to provide a causal framework that permits the identification and estimation of causal effects from observational studies. We begin by providing a causal interpretation for standard exogenous regressors and standard “valid” and “relevant” instrumental variables. We then build on this interpretation to characterize extended instrumental variables (EIV) methods, that is methods that make use of variables that need not be valid instruments in the standard sense, but that are nevertheless instrumental in the recovery of causal effects of interest. After examining special cases of single and double EIV methods, we provide necessary and sufficient conditions for the identification of causal effects by means of EIV and provide consistent and asymptotically normal estimators for the effects of interest.

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For nearly a century, investigators in the social sciences have used regression models to deduce cause-and-effect relationships from patterns of association. Path models and automated search procedures are more recent developments. In my view, this enterprise has not been successful. The models tend to neglect the difficulties in establishing causal relations, and the mathematical complexities tend to obscure rather than clarify the assumptions on which the analysis is based. Formal statistical inference is, by its nature, conditional. If maintained hypotheses A, B, C,... hold, then H can be tested against the data. However, if A, B, C,... remain in doubt, so must inferences about H. Careful scrutiny of maintained hypotheses should therefore be a critical part of empirical work-- a principle honored more often in the breach than the observance.

This paper (which is mainly expository) sets up graphical models for causation, having a bit less than the usual complement of hypothetical counterfactuals. Assuming the invariance of error distributions may be essential for causal inference, but the errors themselves need not be invariant. Graphs can be interpreted using conditional distributions, so that we can better address connections between the mathematical framework and causality in the world. The identification problem is posed in terms of conditionals. As will be seen, causal relationships cannot be inferred from a data set by running regressions unless there is substantial prior knowledge about the mechanisms that generated the data. There are few successful applications of graphical models, mainly because few causal pathways can be excluded on a priori grounds. The invariance conditions themselves remain to be assessed.

To explain how stimuli cause consciousness, we have to explain causality. We can't trace linear causal chains from receptors after the first cortical synapse, so we use circular causality to explain neural pattern formation by self-organizing dynamics. But an aspect of intentional action is causality, which we extrapolate to material objects in the world. Thus causality is a property of mind, not matter.