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52
Learning Bayesian networks: The combination of knowledge and statistical data
 Machine Learning
, 1995
"... We describe scoring metrics for learning Bayesian networks from a combination of user knowledge and statistical data. We identify two important properties of metrics, which we call event equivalence and parameter modularity. These properties have been mostly ignored, but when combined, greatly simpl ..."
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Cited by 1158 (35 self)
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We describe scoring metrics for learning Bayesian networks from a combination of user knowledge and statistical data. We identify two important properties of metrics, which we call event equivalence and parameter modularity. These properties have been mostly ignored, but when combined, greatly simplify the encoding of a user’s prior knowledge. In particular, a user can express his knowledge—for the most part—as a single prior Bayesian network for the domain. 1
A Tutorial on Learning Bayesian Networks
 Communications of the ACM
, 1995
"... We examine a graphical representation of uncertain knowledge called a Bayesian network. The representation is easy to construct and interpret, yet has formal probabilistic semantics making it suitable for statistical manipulation. We show how we can use the representation to learn new knowledge by c ..."
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Cited by 365 (12 self)
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We examine a graphical representation of uncertain knowledge called a Bayesian network. The representation is easy to construct and interpret, yet has formal probabilistic semantics making it suitable for statistical manipulation. We show how we can use the representation to learn new knowledge by combining domain knowledge with statistical data. 1 Introduction Many techniques for learning rely heavily on data. In contrast, the knowledge encoded in expert systems usually comes solely from an expert. In this paper, we examine a knowledge representation, called a Bayesian network, that lets us have the best of both worlds. Namely, the representation allows us to learn new knowledge by combining expert domain knowledge and statistical data. A Bayesian network is a graphical representation of uncertain knowledge that most people find easy to construct and interpret. In addition, the representation has formal probabilistic semantics, making it suitable for statistical manipulation (Howard,...
A new look at causal independence
 In Proc. of the Tenth Conference on Uncertainty in Artificial Ingelligence
, 1994
"... Heckerman (1993) defined causal independence in terms of a set of temporal conditional independence statements. These statements formalized certain types of causal interaction where (1) the effect is independent of the order that causes are introduced and (2) the impact of a single cause on the effe ..."
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Cited by 76 (4 self)
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Heckerman (1993) defined causal independence in terms of a set of temporal conditional independence statements. These statements formalized certain types of causal interaction where (1) the effect is independent of the order that causes are introduced and (2) the impact of a single cause on the effect does not depend on what other causes have previously been applied. In this paper, we introduce an equivalent atemporal characterization of causal independence based on a functional representation of the relationship between causes and the effect. In this representation, the interaction between causes and effect can be written as a nested decomposition of functions. Causal independence can be exploited by representing this decomposition in the belief network, resulting in representations that are more efficient for inference than general causal models. We present empirical results showing the benefits of a causalindependence representation for beliefnetwork inference. 1
Axiomatizing causal reasoning
 Uncertainty in Artificial Intelligence
, 1998
"... Causal models defined in terms of a collection of equations, as defined by Pearl, are axiomatized here. Axiomatizations are provided for three successively more general classes of causal models: (1) the class of recursive theories (those without feedback), (2) the class of theories where the solutio ..."
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Cited by 76 (7 self)
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Causal models defined in terms of a collection of equations, as defined by Pearl, are axiomatized here. Axiomatizations are provided for three successively more general classes of causal models: (1) the class of recursive theories (those without feedback), (2) the class of theories where the solutions to the equations are unique, (3) arbitrary theories (where the equations may not have solutions and, if they do, they are not necessarily unique). It is shown that to reason about causality in the most general third class, we must extend the language used by Galles and Pearl (1997, 1998). In addition, the complexity of the decision procedures is characterized for all the languages and classes of models considered. 1.
Counterfactual Probabilities: Computational Methods, Bounds and Applications
 UNCERTAINTY IN ARTIFICIAL INTELLIGENCE
, 1994
"... Evaluation of counterfactual queries (e.g., "If A were true, would C have been true?") is important to fault diagnosis, planning, and determination of liability. In this paper we present methods for computing the probabilities of such queries using the formulation proposed in [Balke and P ..."
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Cited by 61 (23 self)
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Evaluation of counterfactual queries (e.g., "If A were true, would C have been true?") is important to fault diagnosis, planning, and determination of liability. In this paper we present methods for computing the probabilities of such queries using the formulation proposed in [Balke and Pearl, 1994], where the antecedent of the query is interpreted as an external action that forces the proposition A to be true. When a prior probability is available on the causal mechanisms governing the domain, counterfactual probabilities can be evaluated precisely. However, when causal knowledge is specified as conditional probabilities on the observables, only bounds can computed. This paper develops techniques for evaluating these bounds, and demonstrates their use in two applications: (1) the determination of treatment efficacy from studies in which subjects may choose their own treatment, and (2) the determination of liability in productsafety litigation.
Probabilistic Evaluation of Counterfactual Queries
 IN PROCEEDINGS AAAI94
, 1994
"... Evaluation of counterfactual queries (e.g., "If A were true, would C have been true?") is important to fault diagnosis, planning, and determination of liability. We present a formalism that uses probabilistic causal networks to evaluate one's belief that the counterfactual consequent, ..."
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Cited by 57 (21 self)
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Evaluation of counterfactual queries (e.g., "If A were true, would C have been true?") is important to fault diagnosis, planning, and determination of liability. We present a formalism that uses probabilistic causal networks to evaluate one's belief that the counterfactual consequent, C, would have been true if the antecedent, A, were true. The antecedent of the query is interpreted as an external action that forces the proposition A to be true, which is consistent with Lewis' Miraculous Analysis. This formalism offers a concrete embodiment of the "closest world" approach which (1) properly reflects common understanding of causal influences, (2) deals with the uncertainties inherent in the world, and (3) is amenable to machine representation.
Reasoning With Cause And Effect
, 1999
"... 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 IJCAI99, and is intended to supplement the lecture with technical details and pointers to mo ..."
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Cited by 40 (0 self)
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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 IJCAI99, 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...
Canonical probabilistic models for knowledge engineering
, 2000
"... The hardest task in knowledge engineering for probabilistic graphical models, such as Bayesian networks and influence diagrams, is obtaining their numerical parameters. Models based on acyclic directed graphs and composed of discrete variables, currently most common in practice, require for every va ..."
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Cited by 39 (14 self)
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The hardest task in knowledge engineering for probabilistic graphical models, such as Bayesian networks and influence diagrams, is obtaining their numerical parameters. Models based on acyclic directed graphs and composed of discrete variables, currently most common in practice, require for every variable a number of parameters that is exponential in the number of its parents in the graph, which makes elicitation from experts or learning from databases a daunting task. In this paper, we review the so called canonical models, whose main advantage is that they require much fewer parameters. We propose a general framework for them, based on three categories: deterministic models, ICI models, and simple canonical models. ICI models rely on the concept of independence of causal influence and can be subdivided into noisy and leaky. We then analyze the most common families of canonical models (the OR/MAX, the AND/MIN, and the noisy XOR), generalizing them and offering criteria for applying them in practice. We also briefly review temporal
Elicitation of Probabilities for Belief Networks: Combining Qualitative and . . .
 IN UNCERTAINTY IN ARTIFICIAL INTELLIGENCE (95): PROCEEDINGS OF THE 11TH CONFERENCE, LOS ALTOS CA
, 1995
"... Although the usefulness of belief networks for reasoning under uncertainty is widely accepted, obtaining numerical probabilities that they require is still perceived a major obstacle. Often not enough statistical data is available to allow for reliable probability estimation. Available informa ..."
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Cited by 36 (3 self)
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Although the usefulness of belief networks for reasoning under uncertainty is widely accepted, obtaining numerical probabilities that they require is still perceived a major obstacle. Often not enough statistical data is available to allow for reliable probability estimation. Available information may not be directly amenable for encoding in the network. Finally, domain experts may be reluctant to provide numerical probabilities. In this paper, we propose a method for elicitation of probabilities from a domain expert that is noninvasive and accommodates whatever probabilistic information the expert is willing to state. We express all available information, whether qualitative or quantitative in nature, in a canonical form consisting of (in)equalities expressing constraints on the hyperspace of possible joint probability distributions. We then use this canonical form to derive secondorder probability distributions over the desired probabilities.
Some properties of joint probability distributions, in
 Proceedings of the 10th Conference on Uncertainty in Artificial 6 Intelligence, UAI94
, 1994
"... Abstract Several Artifi cial Intelligence schemes for reasoning under uncertainty explore either explicitly or implicitly asymmetries among probabilities of various states of their uncer tain domain models. Even though the correct working of these schemes is practically con tingent upon the existen ..."
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Cited by 29 (7 self)
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Abstract Several Artifi cial Intelligence schemes for reasoning under uncertainty explore either explicitly or implicitly asymmetries among probabilities of various states of their uncer tain domain models. Even though the correct working of these schemes is practically con tingent upon the existence of a small number of probable states, no formal justification has been proposed of why this should be the case. This paper attempts to fill this apparent gap by studying asymmetries among probabili ties of various states of uncertain models. By rewriting the joint probability distribu tion over a model's variables into a product of individual variables' prior and conditional probability distributions and applying cen tral limit theorem to this product, we can demonstrate that the probabilities of indi vidual states of the model can be expected to be drawn from highly skewed lognormal distributions. With sufficient asymmetry in individual prior and conditional probability distributions, a small fraction of states can be expected to cover a large portion of the total probability space with the remaining states having practically negligible probabil ity. Theoretical discussion is supplemented by simulation results and an illustrative real world example.