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5th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems Paris, France, July 4–8, 1994 Selected Papers
Bayes nets are seeing increasing use in expert systems [2, 6], and structural equations models continue to be popular in many branches of the social sciences [1]. Both types of models involve directed acyclic graphs with variables as nodes, and in both cases there is much mysterious talk about causal interpretation. This paper uses probability trees to give precise conditions under which Bayes nets...
Survey of the mathematical models proposed to represent quantified beliefs, and their comparison. The models considered are separated into non standard probability and non probability models, according to the fact they are based on probability theory or not. The first group concerns the upper and lower probability models, the second the possibility theory and the transferable belief model.
The Dempster-Shafer theory of evidence is developed in a very general setting. Its algebraic part is discussed as a body of arguments which contains an allocation of support and an allowment of possibility for each hypothesis. A rule of combination of bodies of arguments is defined which constitutes the symbolic counterpart of Dempster's rule. Bodies of evidence are introduced by assigning probabilities...
There are described some algebraic structures on a space of belief functions on a two-element frame, namely so called Dempster's semigroup (with Dempster's operation ⊕), dempsteroids, and their basic properties. The present paper is devoted to the investigation of automorphisms of Dempster's semigroup. Full characterization of general and ordered automorphisms is obtained, their parametric description...
Coherence is an important concept which is introduced and discussed in a new mathematics branch, Imprecise Probability Theory. By using the Choquet integral, belief measures can be extended to be coherent lower previsions on the linear space consisting of all bounded functions. As a special case, we establish that all belief measures are coherent imprecise probabilities.
In this paper, we use the belief functions framework to represent the available information in a decision making problem. We start by presenting the related decision process. Then, we define and caracterize the supporting knowledge of a decision. Finally, we give an evaluation of the confidence in a decision that is supported by a given knowledge.
We introduce a methodology for performing approximate computations in complex probabilistic expert systems, when some components can be handled exactly and others require approximation or simulation. This is illustrated by means of a modified version of the familiar ‘chest-clinic’ problem.
Different uncertainty propagation algorithms in graphical structures can be viewed as a particular case of propagation in a joint tree, which can be obtained from different triangulations of the original graph. The complexity of the resulting propagation algorithms depends on the size of the resulting triangulated graph. The problem of obtaining an optimum graph triangulation is known to be NP-complete...
Local computational techniques have been proposed to compute marginals for the variables in belief networks or valuation networks, based on the secondary structures called clique trees or Markov trees. However, these techniques only compute the marginal on the subset of variables contained in one node of the secondary structure. This paper presents a method for computing the marginal on the subset...
This paper suggests a representation of Bayesian networks based on a generalized relational database model. The main advantage of this representation is that it takes full advantage of the capabilities of conventional relational database systems for probabilistic inference. Belief update, for example, can be processed as an ordinary query, and the techniques for query optimization are directly applicable...
In this paper, decision influence diagrams are studied when the assessment of utilities with real numerical values is considered to be too restrictive, and the use of fuzzy sets to model the problem in terms of fuzzy utilities seems appropiate. An algorithm to solve decision influence diagrams with fuzzy utilities is suggested.
Causal Networks have recently received much attention in AI, and have been used in many areas as a knowledge representation. First, from the knowledge engineering point of view, we present causal networks, introduce a concept of network parameters, propose some principles for construction and use of causal networks, and indicate the advantages of the knowledge bases with the form of causal networks...
Once causal networks have been chosen as the model of knowledge representation of our interest, the aim of this work is to assess the performance of polytrees or Singly connected Causal Networks (SCNs) as approximations of general Multiply connected Causal Networks (MCNs). To do that we have carried out a simulation experiment in which we generated a number of MCNs, simulated them to get samples and...
In this paper, we introduce evidence propagation operations on influence diagrams and a concept of value of evidence, which measures the value of experimentation. Evidence propagation operations are critical for the computation of the value of evidence, general update and inference operations in normative expert systems which are based on the influence diagram (Bayesian Network) paradigm. The value...
In this essay I present a general characterization of qualitative probability, defining the concept of a qualitative probability language and proposing some bases for comparison. In particular, enumerating some of the distinctions that can be supported by a qualitative probability language induces a partial taxonomy of possible approaches. I discuss some of these in further depth, identify central...
We introduce a new application of qualitative models of uncertainty. The qualitative analysis of a numerical model of uncertainty reveals the qualitative behaviour of that model when new evidence is obtained. This behaviour can be compared with an expert's specifications to identify those situations in which the model does not behave as expected. We report the result of experiments performed using...
We study probability intervals as a interesting tool to represent uncertain information. Basic concepts for the management of uncertain information, as combination, marginalization, conditioning and integration are considered for probability intervals. Moreover, the relationships of this theory with some others, as lower and upper probabilities and Choquet capacities of order two are also clarified...
In this paper, given an arbitrary finite family of conditional events F, a generalized probabilistic knowledge base represented by a set of conditional probability bounds defined on F is considered. Following the approach of de Finetti we define the concept of coherence for the given set of bounds. Then, some results on the probabilistic consistency of the knowledge base are obtained. Finally, an...
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