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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 a ..."
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Cited by 117 (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
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 38 (14 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 19 (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...
From Imaging and Stochastic Control to a Calculus of Actions
"... This paper highlights relationships among stochastic control theory, Lewis' notion of "imaging", and the representation of actions in AI systems. We show that the language of causal graphs offers a practical solution to the frame problem and its two satellites: the ramification and co ..."
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Cited by 1 (0 self)
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This paper highlights relationships among stochastic control theory, Lewis' notion of "imaging", and the representation of actions in AI systems. We show that the language of causal graphs offers a practical solution to the frame problem and its two satellites: the ramification and concurrency problems. Finally, we present a symbolic machinery that admits both probabilistic and causal information and produces probabilistic statements about the effect of actions and the impact of observations. 1 Representing and Revising Probability Functions Engineers consider the theory of stochastic control as the basic paradigm in the design and analysis of systems operating in uncertain environments. Knowledge in stochastic control theory is represented by a function P (s), which measures the probability assigned to each state s of the world, at any given time. Given P (s), it is possible to calculate the probability of any conceivable event E, by simply summing up P (s) over all states that entai...
How to Understand the Foundations of Empirical Belief in a
"... The discussion between foundationalism and coherentism has been around for a long time, but for about two decades it has, in a way, become more serious than before, currently forming one of the central epistemological issues. It starts from the wellknown justification trilemma which runs as follows: ..."
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The discussion between foundationalism and coherentism has been around for a long time, but for about two decades it has, in a way, become more serious than before, currently forming one of the central epistemological issues. It starts from the wellknown justification trilemma which runs as follows:
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,...