This literature review discusses different methods under the general rubric of learning Bayesian networks from data, and includes some overlapping work on more general probabilistic networks. Connections are drawn between the statistical, neural network, and uncertainty communities, and between the different methodological communities, such as Bayesian, description length, and classical statistics. Basic concepts for learning and Bayesian networks are introduced and methods are then reviewed. Methods are discussed for learning parameters of a probabilistic network, for learning the structure, and for learning hidden variables. The presentation avoids formal definitions and theorems, as these are plentiful in the literature, and instead illustrates key concepts with simplified examples. Keywords--- Bayesian networks, graphical models, hidden variables, learning, learning structure, probabilistic networks, knowledge discovery. I. Introduction Probabilistic networks or probabilistic gra...

The ramification problem in the context of commonsense reasoning about actions and change names the challenge to accommodate actions whose execution causes indirect effects. Not being part of the respective action specification, such effects are consequences of general laws describing dependencies between components of the world description. We present a general approach to this problem which incorporates causality, formalized by directed relations between two single effects stating that, under specific circumstances, the occurrence of the first causes the second. Moreover, necessity of exploiting causal information in this way or a similar is argued by elaborating the limitations of common paradigms employed to handle ramifications, namely, the principle of categorization and the policy of minimal change. Our abstract solution is exemplarily integrated into a specific calculus based on the logic programming paradigm. To apper in: Artificial Intelligence Journal On leave from FG Inte...

The primary aim of this paper is to show how graphical models can be used as a mathematical language for integrating statistical and subject-matter information. In particular, the paper develops a principled, nonparametric framework for causal inference, in which diagrams are queried to determine if the assumptions available are sufficient for identifying causal effects from nonexperimental data. If so the diagrams can be queried to produce mathematical expressions for causal effects in terms of observed distributions; otherwise, the diagrams can be queried to suggest additional observations or auxiliary experiments from which the desired inferences can be obtained. Key words: Causal inference, graph models, interventions treatment effect 1 Introduction The tools introduced in this paper are aimed at helping researchers communicate qualitative assumptions about cause-effect relationships, elucidate the ramifications of such assumptions, and derive causal inferences from a combination...

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This paper concerns the assessment of the effects of actions or policy interventions from a combination of: (i) nonexperimental data, and (ii) substantive assumptions. The assumptions are encoded in the form of a directed acyclic graph, also called "causal graph", in which some variables are presumed to be unobserved. The paper establishes a necessary and sufficient criterion for the identifiability of the causal effects of a singleton variable on all other variables in the model, and a powerful sufficient criterion for the effects of a singleton variable on any set of variables.

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...

Introduction The introduction of Bayesian networks (Pearl 1986b) and associated local computation algorithms (Lauritzen and Spiegelhalter 1988, Shenoy and Shafer 1990, Jensen, Lauritzen and Olesen 1990) has initiated a renewed interest for understanding causal concepts in connection with modelling complex stochastic systems. It has become clear that graphical models, in particular those based upon directed acyclic graphs, have natural causal interpretations and thus form a base for a language in which causal concepts can be discussed and analysed in precise terms. As a consequence there has been an explosion of writings, not primarily within mainstream statistical literature, concerned with the exploitation of this language to clarify and extend causal concepts. Among these we mention in particular books by Spirtes, Glymour and Scheines (1993), Shafer (1996), and Pearl (2000) as well as the collection of papers in Glymour and Cooper (1999). Very briefly, but fundamentally,

We present a definition of cause and effect in terms of decision-theoretic primitives and thereby provide a principled foundation for causal reasoning. Our definition departs from the traditional view of causation in that causal assertions may vary with the set of decisions available. We argue that this approach provides added clarity to the notion of cause. Also in this paper, we examine the encoding of causal relationships in directed acyclic graphs. We describe a special class of influence diagrams, those in canonical form, and show its relationship to Pearl's representation of cause and effect. Finally, we show how canonical form facilitates counterfactual reasoning. 1. Introduction Knowledge of cause and effect is crucial for modeling the affects of actions. For example, if we observe a statistical correlation between smoking and lung cancer, we can not conclude from this observation alone that our chances of getting lung cancer will change if we stop smoking. If, however, we als...

Structural equation modeling (SEM) has dominated causal analysis in the social and behavioral sciences since the 1960s. Currently, many SEM practitioners are having difficulty articulating the causal content of SEM and are seeking foundational answers.

Chain graphs are a natural generalization of directed acyclic graphs (DAGs) and undirected graphs. However, the apparent simplicity of chain graphs belies the subtlety of the conditional independence hypotheses that they represent. There are a number of simple and apparently plausible, but ultimately fallacious interpretations of chain graphs that are often invoked, implicitly or explicitly. These interpretations also lead to awed methods for applying background knowledge to model selection. We present a valid interpretation by showing how the distribution corresponding to a chain graph may be generated as the equilibrium distribution of dynamic models with feedback. These dynamic interpretations lead to a simple theory of intervention, extending the theory developed for DAGs. Finally, we contrast chain graph models under this interpretation with simultaneous equation models which have traditionally been used to model feedback in econometrics. Keywords: Causal model; cha...