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Graphical Models, Causality, And Intervention
, 1993
"... tion of belief networks is given in [4]. 2 In [3], the graphs were called "causal networks," for which the authors were criticised; they have agreed to refrain from using the word "causal." In the current paper, Spiegelhalter etal. deemphasize the causal interpretation of the arcs in favor of the ..."
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Cited by 97 (35 self)
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tion of belief networks is given in [4]. 2 In [3], the graphs were called "causal networks," for which the authors were criticised; they have agreed to refrain from using the word "causal." In the current paper, Spiegelhalter etal. deemphasize the causal interpretation of the arcs in favor of the "irrelevance" interpretation (page 4). I think this retreat is regrettable for two reasons: first, causal associations are the primary source of judgments about irrelevance and, second, rejecting the causal interpretation of arcs prevents us from using graphical models for making legitimate predictions about the effect of actions. Such predictions are indispensable in applications such as treatment management and patient monitoring. the causal model also tells us how these probabilities would change as a result of external interventions in the system. For this reason, causal models (or "structural models" as they are often called) have been the target of relent
DecisionTheoretic Foundations for Causal Reasoning
 Journal of Artificial Intelligence Research
, 1995
"... We present a definition of cause and effect in terms of decisiontheoretic 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 ..."
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Cited by 54 (8 self)
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We present a definition of cause and effect in terms of decisiontheoretic 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...
A Probabilistic Calculus of Actions
, 1994
"... We present a symbolic machinery that admits both probabilistic and causal information about a given domain, and produces probabilistic statements about the effect of actions and the impact of observations. The calculus admits two types of conditioning operators: ordinary Bayes conditioning, P (yj ..."
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Cited by 30 (13 self)
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We present a symbolic machinery that admits both probabilistic and causal information about a given domain, and produces probabilistic statements about the effect of actions and the impact of observations. The calculus admits two types of conditioning operators: ordinary Bayes conditioning, P (yjX = x), which represents the observation X = x, and causal conditioning, P (yjdo(X = x)), read: the probability of Y = y conditioned on holding X constant (at x) by deliberate action. Given a mixture of such observational and causal sentences, together with the topology of the causal graph, the calculus derives new conditional probabilities of both types, thus enabling one to quantify the effects of actions and observations. 1 Introduction Probabilistic methods, especially those based on graphical models have proven useful in tasks of predictions, abduction and belief revision [Pearl 1988, Heckerman 1990, Goldszmidt 1992, Darwiche 1993]. Their use in planning, however, remains less po...
Aspects Of Graphical Models Connected With Causality
, 1993
"... This paper demonstrates the use of graphs as a mathematical tool for expressing independenices, and as a formal language for communicating and processing causal information in statistical analysis. We show how complex information about external interventions can be organized and represented graphica ..."
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Cited by 13 (10 self)
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This paper demonstrates the use of graphs as a mathematical tool for expressing independenices, and as a formal language for communicating and processing causal information in statistical analysis. We show how complex information about external interventions can be organized and represented graphically and, conversely, how the graphical representation can be used to facilitate quantitative predictions of the effects of interventions. We first review the Markovian account of causation and show that directed acyclic graphs (DAGs) offer an economical scheme for representing conditional independence assumptions and for deducing and displaying all the logical consequences of such assumptions. We then introduce the manipulative account of causation and show that any DAG defines a simple transformation which tells us how the probability distribution will change as a result of external interventions in the system. Using this transformation it is possible to quantify, from nonexperimental data...
On The Identification Of Nonparametric Structural Models
, 1997
"... In this paper we study the identifiability of nonparametric models, that is, models in which both the functional forms of the equations and the probability distributions of the disturbances remain unspecified. Identifiability in such models does not mean uniqueness of parameters but rather uniquenes ..."
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Cited by 2 (1 self)
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In this paper we study the identifiability of nonparametric models, that is, models in which both the functional forms of the equations and the probability distributions of the disturbances remain unspecified. Identifiability in such models does not mean uniqueness of parameters but rather uniqueness of the set of predictions of interest to the investigator. For example, predicting the effects of changes, interventions, and control. We provide sufficient and necessary conditions for identifying a set of causal predictions of the type: "Find the distribution of Y , assuming that X is controlled by external intervention", where Y and X are arbitrary variables of interest. Whenever identifiable, such predictions can be expressed in closed algebraic form, in terms of observed distributions. We also show how the identifying criteria can be verified qualitatively, by inspection, using the graphical representation of the structural model. When compared to standard identifiability tests of lin...
E01] The Ensemble project, 2001. Available electronically at http://www.cs.cornell.edu/Info/Projects/Ensemble
, 2002
"... novel representation: ..."
Optimal Control of Dynamic Systems by Decomposition and Aggregation
"... The paper is concerned with the reduction of a class of optimal control problems to simpler problems by using decomposition and aggregation. Decomposition is shown to provide a good approximation when the system dynamics involve a nearly decomposable matrices or variables with strong and weak intera ..."
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The paper is concerned with the reduction of a class of optimal control problems to simpler problems by using decomposition and aggregation. Decomposition is shown to provide a good approximation when the system dynamics involve a nearly decomposable matrices or variables with strong and weak interactions. Aggregation provides a good approximation if each of the decomposed matrix has one or more dominant eigenvalues. It is shown how one can construct nearly optimal controls for the given system from the optimal solutions of the simpler reduced problems. This work was partly supported by NSERC Grant A4619. Constructive comments from Herb Simon are very much appreciated. y Faculty of Management, University of Toronto, Toronto, Ontario, Canada M5S 1V4 z Department of Mathematics, University of Georgia, Athens, GA 30602 1 Introduction According to Herbert A. Simon (1977), almost all complex systems that occur in nature exhibit an underlying hierarchic structure. Simon provides bot...
(Draft Copy) On the Statistical Interpretation of Structural Equations
"... F28.92> y 2 and x 1 were fixed" using the model described in (1), the result does not match the interpretation advanced by Goldberger. Specifically, assuming u 1 and u 2 are zeromean disturbances (independent on X 1 and X 2 ), Wermuth finds E(Y 1 j Y 2 = y 2 ; X 1 = x 1 ) 6= a 1 y 2 + a 2 x 1 (u ..."
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F28.92> y 2 and x 1 were fixed" using the model described in (1), the result does not match the interpretation advanced by Goldberger. Specifically, assuming u 1 and u 2 are zeromean disturbances (independent on X 1 and X 2 ), Wermuth finds E(Y 1 j Y 2 = y 2 ; X 1 = x 1 ) 6= a 1 y 2 + a 2 x 1 (unless further assumptions are made) and concludes that "the parameters in (1) cannot have the meaning Arthur Goldberger claims they have." 1 This exchange between a statistician and an economist exemplifies the long history of tension between regression analysis and structural equations modeling, which dates back to the inception of the latter by Wright [27],
A Causal Calculus
"... Given an arbitrary causal graph, some of whose nodes are observable and some unobservable, the problem is to determine whether the causal effect of one variable on another can be computed from the joint distribution over the observables and, if the answer is positive, to derive a formula for the ..."
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Given an arbitrary causal graph, some of whose nodes are observable and some unobservable, the problem is to determine whether the causal effect of one variable on another can be computed from the joint distribution over the observables and, if the answer is positive, to derive a formula for the causal effect. We introduce a calculus which, using a step by step reduction of probabilistic expressions, derives the desired formulas. 1 1 Introduction Networks employing directed acyclic graphs (DAGs) can be used to provide either 1. an economical scheme for representing conditional independence assumptions and joint distribution functions, or 2. a graphical language for representing causal influences. Although the professed motivation for investigating such models lies primarily in the second category, [Wright, 1921, Blalock, 1971, Simon, 1954, Pearl 1988], causal inferences have been treated very cautiously in the statistical literature [Lauritzen & Spiegelhalter 1988, Cox 1992,...