Abstract. Graphical models provide a framework for exploration of multivariate dependence patterns. The connection between graph and statistical model is made by identifying the vertices of the graph with the observed variables and translating the pattern of edges in the graph into a pattern of conditional independences that is imposed on the variables ’ joint distribution. Focusing on Gaussian models, we review classical graphical models. For these models the defining conditional independences are equivalent to vanishing of certain (partial) correlation coefficients associated with individual edges that are absent from the graph. Hence, Gaussian graphical model selection can be performed by multiple testing of hypotheses about vanishing (partial) correlation coefficients. We show and exemplify how this approach allows one to perform model selection while controlling error rates for incorrect edge inclusion. Key words and phrases: Acyclic directed graph, Bayesian network, bidirected graph, chain graph, concentration graph, covariance graph, DAG, graphical model, multiple testing, undirected graph. 1.

Given a set of random variables, it is often the case that their associations can be explained by hidden common causes. We present a set of well-defined assumptions and a provably correct algorithm that allow us to identify some of such hidden common causes. The assumptions are fairly general and sometimes weaker than those used in practice by, for instance, econometricians, psychometricians, social scientists and in many other fields where latent variable models are important and tools such as factor analysis are applicable. The goal is automated knowledge discovery: identifying latent variables that can be used across diferent applications and causal models and throw new insights over a data generating process. Our approach is evaluated throught simulations and three real-world cases.

Intelligent systems in an open world must reason about many interacting entities related to each other in diverse ways and having uncertain features and relationships. Traditional probabilistic languages lack the expressive power to handle relational domains. Classical first-order logic is sufficiently expressive, but lacks a coherent plausible reasoning capability. Recent years have seen the emergence of a variety of approaches to integrating first-order logic, probability, and machine learning. This paper presents Multi-entity Bayesian networks (MEBN), a formal system that integrates First Order Logic (FOL) with Bayesian probability theory. MEBN extends ordinary

We formulate the problem of learning and comparing the effects of dynamic treatment strategies in a probabilistic decision-theoretic framework, and in particular show how Robins’s “G-computation ” formula arises naturally. Careful attention is paid to the mathematical and substantive conditions necessary to justify use of this formula. Probabilistic influence diagrams are used to simplify manipulations. We compare our approach with formulations based on causal DAGs and on potential response models. Some key words and phrases: Causal inference; G-computation; Influence diagram; Observational study; Potential response; Sequential decision theory; Stability. 1

We reconsider two graphical aids to handling complex mixed masses of evidence in a legal case: Wigmore charts and Bayesian networks. Our aim is to forge a synthesis of their best features, and to develop this further to overcome remaining limitations. One important consideration is the multi-layered nature of a complex case, which can involve direct evidence, ancillary evidence, evidence about ancillary evidence... all of a number of different kinds. If all these features are represented in one diagram, the result can be messy and hard to interpret. In addition there are often recurrent features and patterns of evidence and evidential relations, e.g. credibility processes or match identification (DNA, eyewitness evidence,...) that may appear, in identical or similar form, at many different places within the same network, or within several different networks, and it is wasteful to model these all individually. The recently introduced technology of “object-oriented Bayesian networks ” suggests a way of dealing with these problems. Any network can itself contain instances of other networks, the details of which can be hidden from view until information on their detailed structure is desired. Moreover, generic networks to represent recurrent patterns of evidence can be constructed once and for all, and copied or edited for re-use as needed. We describe the potential of this mode of description to simplify the construction and display of complex legal cases. To facilitate our narrative the celebrated Sacco and Vanzetti murder case is used to illustrate the various methods discussed.

A connectionist model of causal attribution is presented, emphasizing the use of domain-general principles of processing and learning previously employed in models of semantic cognition. The model categorizes objects dependent upon their observed “causal properties ” and is capable of making several types of inferences that four-year-old children have been shown to be capable of. The model gives rise to approximate conformity to normative models of causal inference and gives approximate estimates of the probability that an object presented in an ambiguous situation actually possesses a particular causal power, based on background knowledge and recent observations. It accounts for data from three sets of experimental studies of the causal inferencing abilities of young children. The model provides a base for further efforts to delineate the intuitive mechanisms of causal inference employed by children and adults, without appealing to inherent principles or mechanisms specialized for causal as opposed to other forms of reasoning.

This paper unifies three complementary approaches to defining, identifying, and estimating causal effects: the classical structural equations approach of the Cowles Commision; the treatment effects framework of Rubin (1974) and Rosenbaum and Rubin (1983); and the Directed Acyclic Graph (DAG) approach of Pearl. The settable system framework nests these prior approaches, while affording significant improvements to each. For example, the settable system approach permits identification of causal effects without requiring exogenous instruments; instead, a weaker conditional exogeneity condition suffices. It removes the stable unit treatment value assumption of the treatment effect approach and provides significant insight into the selection of covariates. It generalizes the DAG ap-proach by accommodating mutual causality and attributes. We provide a variety of results ensuring structural identification of general covariate-conditioned average causal effects, laying the founda-tion for parametric and nonparametric estimation of effects of interest and new tests for structural identification.

This paper unifies three complementary approaches to defining, identifying, and estimating causal effects: the classical structural equations approach of the Cowles Commision; the treatment effects framework of Rubin (1974) and Rosenbaum and Rubin (1983); and the Directed Acyclic Graph (DAG) approach of Pearl. The settable system framework nests these prior approaches, while affording significant improvements to each. For example, the settable system approach permits identification and estimation of causal effects without requiring exogenous instruments, generalizing the classical structural equations approach; it relaxes the stable unit treatment value assumption of the treatment effect approach and provides significant insight into the selection of covariates; and it accommodates mutual causality, generalizing the DAG approach. We provide necessary and sufficient conditions for identification of covariate-conditioned average causal effects, parametric and nonparametric estimation results, and new tests for unconfoundedness.

We consider the problem of incomplete conditional probability tables in Bayesian nets, noting that marginal probabilities for an effect, given single cause are usually easy to elicit and can serve as constraints on the full CPT. A form of maximum entropy principle, local to an effect node is developed and contrasted with existing global methods. Exact maximum-entropy CPTs are computed and a conjecture about the exact solution for eects with a general number N of causes is examined.

We consider the problems arising from using sequences of experiments to discover the causal structure among a set of variables, none of whom are known ahead of time to be an “outcome”. In particular, we present various approaches to resolve conflicts in the experimental results arising from sampling variability in the experiments. We provide a sufficient condition that allows for pooling of data from experiments with different joint distributions over the variables. Satisfaction of the condition allows for more powerful independence tests that may resolve some of the conflicts in the experimental results. The pooling condition has its own problems, but should – due to its generality – be informative to techniques for meta-analysis. 1.