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68
Learning Bayesian Networks is NPHard
, 1994
"... Algorithms for learning Bayesian networks from data have two components: a scoring metric and a search procedure. The scoring metric computes a score reflecting the goodnessoffit of the structure to the data. The search procedure tries to identify network structures with high scores. Heckerman et ..."
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Cited by 194 (2 self)
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Algorithms for learning Bayesian networks from data have two components: a scoring metric and a search procedure. The scoring metric computes a score reflecting the goodnessoffit of the structure to the data. The search procedure tries to identify network structures with high scores. Heckerman et al. (1994) introduced a Bayesian metric, called the BDe metric, that computes the relative posterior probability of a network structure given data. They show that the metric has a property desireable for inferring causal structure from data. In this paper, we show that the problem of deciding whether there is a Bayesian networkamong those where each node has at most k parentsthat has a relative posterior probability greater than a given constant is NPcomplete, when the BDe metric is used. 1 Introduction Recently, many researchers have begun to investigate methods for learning Bayesian networks, including Bayesian methods [Cooper and Herskovits, 1991, Buntine, 1991, York 1992, Spiegel...
A Review of Explanation Methods for Bayesian Networks
 Knowledge Engineering Review
, 2000
"... One of the key factors for the acceptance of expert systems in real world domains is the capability to explain their reasoning. This paper describes the basic properties that characterize explanation methods and reviews the methods developed up to date for explanation in Bayesian networks. ..."
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Cited by 48 (5 self)
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One of the key factors for the acceptance of expert systems in real world domains is the capability to explain their reasoning. This paper describes the basic properties that characterize explanation methods and reviews the methods developed up to date for explanation in Bayesian networks.
Qualitative Verbal Explanations in Bayesian Belief Networks
, 1996
"... Application of Bayesian belief networks in systems that interact directly with human users, such as decision support systems, requires effective user interfaces. The principal task of such interfaces is bridging the gap between probabilistic models and human intuitive approaches to modeling uncer ..."
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Cited by 35 (5 self)
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Application of Bayesian belief networks in systems that interact directly with human users, such as decision support systems, requires effective user interfaces. The principal task of such interfaces is bridging the gap between probabilistic models and human intuitive approaches to modeling uncertainty. We describe several methods for automatic generation of qualitative verbal explanations in systems based on Bayesian belief networks. We show simple techniques for explaining the structure of a belief network model and the interactions among its variables. We also present a technique for generating qualitative explanations of reasoning. Keywords: Explanation, Bayesian belief networks, qualitative probabilistic networks 1 Introduction The purpose of computing is insight, not numbers. Richard Wesley Hamming As the increasing number of successful applications in such domains as diagnosis, planning, learning, vision, and natural language processing demonstrates, Bayesian belief ne...
Intercausal Reasoning with Uninstantiated Ancestor Nodes
 In Proceedings of the Ninth Annual Conference on Uncertainty in Artificial Intelligence (UAI93
, 1993
"... Intercausal reasoning is a common inference pattern involving probabilistic dependence of causes of an observed common effect. The sign of this dependence is captured by a qualitative property called product synergy. The current definition of product synergy is insufficient for intercausal rea ..."
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Cited by 31 (13 self)
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Intercausal reasoning is a common inference pattern involving probabilistic dependence of causes of an observed common effect. The sign of this dependence is captured by a qualitative property called product synergy. The current definition of product synergy is insufficient for intercausal reasoning where there are additional uninstantiated causes of the common effect. We propose a new definition of product synergy and prove its adequacy for intercausal reasoning with direct and indirect evidence for the common effect. The new definition is based on a new property matrix half positive semidefiniteness, a weakened form of matrix positive semidefiniteness. 1
Relevance in probabilistic models: backyards in a small world
 In Working notes of the AAAI1994 Fall Symposium Series: Relevance
"... Each of the variables in a large probabilistic model may be relevant for some types of reasoning within this model, but rarely will all of them participate in reasoning related to a single query. We review a variety of schemes to identify variables that given certain observations are relevant to a q ..."
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Cited by 16 (8 self)
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Each of the variables in a large probabilistic model may be relevant for some types of reasoning within this model, but rarely will all of them participate in reasoning related to a single query. We review a variety of schemes to identify variables that given certain observations are relevant to a query of interest.
Bayesian Network Modelling through Qualitative Patterns
 ARTIFICIAL INTELLIGENCE
, 2003
"... In designing a Bayesian network for an actual problem, developers need to bridge the gap between the mathematical abstractions o#ered by the Bayesiannetwork formalism and the features of the problem to be modelled. Qualitative probabilistic networks (QPNs) have been put forward as qualitative an ..."
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Cited by 15 (5 self)
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In designing a Bayesian network for an actual problem, developers need to bridge the gap between the mathematical abstractions o#ered by the Bayesiannetwork formalism and the features of the problem to be modelled. Qualitative probabilistic networks (QPNs) have been put forward as qualitative analogues to Bayesian networks, and allow modelling interactions in terms of qualitative signs. They thus have the advantage that developers can abstract from the numerical detail, and therefore the gap may not be as wide as for their quantitative counterparts. A notion that has been suggested in the literature to facilitate Bayesiannetwork development is causal independence. It allows exploiting compact representations of probabilistic interactions among variables in a network. In the paper, we deploy both causal independence and QPNs in developing and analysing a collection of qualitative, causal interaction patterns, called QC patterns. These are endowed with a fixed qualitative semantics, and are intended to o#er developers a highlevel starting point when developing Bayesian networks.
Some Varieties of Qualitative Probability
 Proceedings of the 5th International Conference on Information Processing and the Management of Uncertainty
, 1994
"... In this essay I present a general characterization of qualitative probability, including a partial taxonomy of possible approaches. I discuss some of these in further depth, identify central issues, and suggest some general comparisons. 1. Introduction In the standard theory of probability, degree ..."
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Cited by 13 (1 self)
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In this essay I present a general characterization of qualitative probability, including a partial taxonomy of possible approaches. I discuss some of these in further depth, identify central issues, and suggest some general comparisons. 1. Introduction In the standard theory of probability, degrees of belief for events or propositions take values in the real interval [0,1]. From degrees of belief on the primitive propositions, the theory dictates degrees of belief for various compound and conditional propositions, and vice versa. Computational schemes for probabilistic reasoning apply this theory to the automated derivation of degrees of belief for designated propositions of interest given prespecified degrees of belief over some other propositions and some particular conditioning propositions observed or hypothesized. This approach has, among other advantages, those accruing to a well understood and powerful underlying theory. Despite these virtues, many have objected to the straig...
Explanation in Probabilistic Systems: Is It Feasible? Will It Work?
, 1996
"... . Reasoning within such domains as engineering, science, management, or medicine is traditionally based on formal methods employing probabilistic treatment of uncertainty. It seems natural to base artificial reasoning systems in these domains on the normative foundations of probability theory. Two u ..."
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Cited by 13 (2 self)
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. Reasoning within such domains as engineering, science, management, or medicine is traditionally based on formal methods employing probabilistic treatment of uncertainty. It seems natural to base artificial reasoning systems in these domains on the normative foundations of probability theory. Two usual objections to this approach are (1) probabilistic inference is computationally intractable in the worst case, and (2) probability theory is incomprehensible for humans and, hence, probabilistic systems may be hardly usable. The first objection has been addressed effectively in the last decade by a variety of efficient exact and approximate schemes for probabilistic reasoning, applied in several practical systems. In this paper, I review the state of the art with respect to the second objection. First I argue that the observed discrepancies between human and probabilistic reasoning and the anticipated difficulties in building user interfaces are not a good reason for rejecting probabilit...
Belief Propagation in Qualitative Probabilistic Networks
 In International Workshop on Qualitative Reasoning and Decision Technologies
, 1993
"... 1 Introduction Probabilistic reasoning schemes are often criticized for the undue precision they require to represent uncertain knowledge in the form of numerical probabilities. In fact, such criticism is misconceived since probability theory is rooted in qual itative judgments of conditional indep ..."
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Cited by 13 (0 self)
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1 Introduction Probabilistic reasoning schemes are often criticized for the undue precision they require to represent uncertain knowledge in the form of numerical probabilities. In fact, such criticism is misconceived since probability theory is rooted in qual itative judgments of conditional independence and relative likelihood, and there are a wide variety of probabilistic schemes that do not require single point prob abilities. These schemes range in specificity from purely qualitative schemes such as knowledge maps [7], Imaps [9], and qualitative probabilistic networks [13], to schemes allowing partial numerical specification, such as intervals rather than point probabilities [1, 11].
Defining Normative Systems for Qualitative Argumentation
 Practical Reasoning, volume 1085 of Lecture Notes in Computer Science
"... . Inspired by two different approaches to providing a qualitative method for reasoning under uncertaintyqualitative probabilistic networks and systems of argumentationthis paper attempts to combine the advantages of both by defining systems of argumentation that have a probabilistic semantics. ..."
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Cited by 13 (9 self)
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. Inspired by two different approaches to providing a qualitative method for reasoning under uncertaintyqualitative probabilistic networks and systems of argumentationthis paper attempts to combine the advantages of both by defining systems of argumentation that have a probabilistic semantics. 1 Introduction In the last few years there have been a number of attempts to build systems for reasoning under uncertainty that are of a qualitative naturethat is they use qualitative rather than numerical values, dealing with concepts such as increases in belief and the relative magnitude of values. In particular, two types of qualitative system have become well established, namely qualitative probabilistic networks (QPNs) [4, 18], and systems of argumentation [8, 11, 12]. While the former are built as an abstraction of probabilistic networks where the links between nodes are only modelled in terms of the qualitative influence of the parents on the children, and therefore have an under...