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Credal Networks under Maximum Entropy
, 2000
"... We apply the principle of maximum entropy to select a unique joint probability distribution from the set of all joint probability distributions specified by a credal network. In detail, we start by showing that the unique joint distribution of a Bayesian tree coincides with the maximum entropy m ..."
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Cited by 10 (4 self)
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We apply the principle of maximum entropy to select a unique joint probability distribution from the set of all joint probability distributions specified by a credal network. In detail, we start by showing that the unique joint distribution of a Bayesian tree coincides with the maximum entropy model of its conditional distributions. This result, however, does not hold anymore for general Bayesian networks. We thus present a new kind of maximum entropy models, which are computed sequentially. We then show that for all general Bayesian networks, the sequential maximum entropy model coincides with the unique joint distribution. Moreover, we apply the new principle of sequential maximum entropy to interval Bayesian networks and more generally to credal networks. We especially show that this application is equivalent to a number of small local entropy maximizations.
Default Reasoning Using Maximum Entropy and Variable Strength Defaults
, 1999
"... The thesis presents a computational model for reasoning with partial information which uses default rules or information about what normally happens. The idea is to provide a means of filling the gaps in an incomplete world view with the most plausible assumptions while allowing for the retraction o ..."
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Cited by 4 (2 self)
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The thesis presents a computational model for reasoning with partial information which uses default rules or information about what normally happens. The idea is to provide a means of filling the gaps in an incomplete world view with the most plausible assumptions while allowing for the retraction of conclusions should they subsequently turn out to be incorrect. The model can be used both to reason from a given knowledge base of default rules, and to aid in the construction of such knowledge bases by allowing their designer to compare the consequences of his design with his own default assumptions. The conclusions supported by the proposed model are justified by the use of a probabilistic semantics for default rules in conjunction with the application of a rational means of inference from incomplete knowledgethe principle of maximum entropy (ME). The thesis develops both the theory and algorithms for the ME approach and argues that it should be considered as a general theory of default reasoning. The argument supporting the thesis has two main threads. Firstly, the ME approach is tested on the benchmark examples required of nonmonotonic behaviour, and it is found to handle them appropriately. Moreover, these patterns of commonsense reasoning emerge as consequences of the chosen semantics rather than being design features. It is argued that this makes the ME approach more objective, and its conclusions more justifiable, than other default systems. Secondly, the ME approach is compared with two existing systems: the lexicographic approach (LEX) and system Z + . It is shown that the former can be equated with ME under suitable conditions making it strictly less expressive, while the latter is too crude to perform the subtle resolution of default conflict which the ME...
Nonmonotonic reasoning in probabilistics
 ECAI 98
, 1998
"... In probabilistics, reasoning atoptimum entropy (MEreasoning) has proved to be a most sound and consistent method for inference. This paper investigates its properties in the framework of nonmonotonic reasoning. In particular, we show that MEreasoning satis es cumulativity and loop, and we focus on ..."
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Cited by 1 (1 self)
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In probabilistics, reasoning atoptimum entropy (MEreasoning) has proved to be a most sound and consistent method for inference. This paper investigates its properties in the framework of nonmonotonic reasoning. In particular, we show that MEreasoning satis es cumulativity and loop, and we focus on its connection to conditionals. Finally, weintroduce the notion of a universal inferenceoperation to generalize nonmonotonic reasoning, thus providing aframe more appropriate for linking nonmonotonic reasoning with belief revision.
From syntactical to semantical and expedient information − a survey
"... Abstract. In this contribution the frequently meaningless statements in the relevant economy literature, about what is knowledge and what is information, are overcome going back to the roots of information and communication theory. Information and entropy are defined precisely and then the theoretic ..."
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Abstract. In this contribution the frequently meaningless statements in the relevant economy literature, about what is knowledge and what is information, are overcome going back to the roots of information and communication theory. Information and entropy are defined precisely and then the theoretical concept is applied to an AImodel of knowledge processing. The result of this application is a powerful inference mechanism, permitting conclusions from given facts in a conditional environment. A creditworthiness problem for consumer credits demonstrates the performance of information based decision support. Here the external information factor, namely the clients ’ profiles, is transformed into expedient or useful information. This ability of the decision model gives rise to a deep discussion about the value and price of information.
Explaining Default Intuitions Using Maximum Entropy
, 2003
"... While research into default reasoning is extensive and many default intuitions are commonly held, no one system has yet captured all these intuitions nor given a formal account to motivate them. This paper argues that the extended maximum entropy approach which incorporates variable strength defaul ..."
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While research into default reasoning is extensive and many default intuitions are commonly held, no one system has yet captured all these intuitions nor given a formal account to motivate them. This paper argues that the extended maximum entropy approach which incorporates variable strength defaults provides a benchmark for default reasoning that is not only objectively motivated but also satisfies all the accepted default intuitions. It is shown that the behaviour of the approach coincides with a wide range of default intuitions taken from examples in the literature, and can be used to explain why some examples have led to confusion. Moreover, analysing the solutions produced by the maximum entropy approach enables clearer differentiation between the default knowledge they contain and the default inferences required of the reasoning system. This suggests that the maximum entropy approach can be used as a benchmark both for eliciting default knowledge when building a knowledge base and, by comparison, for clarifying the underlying biases of other default reasoning systems. 1