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31
The inferential complexity of Bayesian and credal networks
 In Proceedings of the International Joint Conference on Artificial Intelligence
, 2005
"... This paper presents new results on the complexity of graphtheoretical models that represent probabilities (Bayesian networks) and that represent interval and set valued probabilities (credal networks). We define a new class of networks with bounded width, and introduce a new decision problem for Ba ..."
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Cited by 30 (7 self)
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This paper presents new results on the complexity of graphtheoretical models that represent probabilities (Bayesian networks) and that represent interval and set valued probabilities (credal networks). We define a new class of networks with bounded width, and introduce a new decision problem for Bayesian networks, the maximin a posteriori. We present new links between the Bayesian and credal networks, and present new results both for Bayesian networks (most probable explanation with observations, maximin a posteriori) and for credal networks (bounds on probabilities a posteriori, most probable explanation with and without observations, maximum a posteriori). 1
Heuristic Algorithms for the Triangulation of Graphs
, 1995
"... 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 resu lt ..."
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Cited by 20 (3 self)
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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 resu lting triangulated graph. The prob lem of obtaining an optimum graph triangu lation is known to be NPcomplete. Thus approximate algorithms which find a good triangulation in reasonable time are of particular interest. This work describes and compares several heuristic algorithms developed for this purpose.
Learning Causal Networks from Data: A survey and a new algorithm for recovering possibilistic causal networks
, 1997
"... Introduction Reasoning in terms of cause and effect is a strategy that arises in many tasks. For example, diagnosis is usually defined as the task of finding the causes (illnesses) from the observed effects (symptoms). Similarly, prediction can be understood as the description of a future plausible ..."
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Cited by 19 (5 self)
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Introduction Reasoning in terms of cause and effect is a strategy that arises in many tasks. For example, diagnosis is usually defined as the task of finding the causes (illnesses) from the observed effects (symptoms). Similarly, prediction can be understood as the description of a future plausible situation where observed effects will be in accordance with the known causal structure of the phenomenon being studied. Causal models are a summary of the knowledge about a phenomenon expressed in terms of causation. Many areas of the ap # This work has been partially supported by the Spanish Comission Interministerial de Ciencia y Tecnologia Project CICYTTIC96 0878. plied sciences (econometry, biomedics, engineering, etc.) have used such a term to refer to models that yield explanations, allow for prediction and facilitate planning and decision making. Causal reasoning can be viewed as inference guided by a causation theory. That kind of inference can be further specialised into induc
Robustness analysis of bayesian networks with global neighborhoods
, 1996
"... Robust Bayesian inference is the calculation of posterior probability bounds given perturbations in a probabilistic model. This paper focuses on perturbations that can be expressed locally in Bayesian networks through convex sets of distributions. Two approaches for combination of local models are c ..."
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Cited by 19 (6 self)
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Robust Bayesian inference is the calculation of posterior probability bounds given perturbations in a probabilistic model. This paper focuses on perturbations that can be expressed locally in Bayesian networks through convex sets of distributions. Two approaches for combination of local models are considered. The rst approach takes the largest set of joint distributions that is compatible with the local sets of distributions; we show how to reduce this type of robust inference to a linear programming problem. The second approach takes the convex hull of joint distributions generated from the local sets of distributions; we demonstrate how to apply interiorpoint optimization methods to generate posterior bounds and how to generate approximations that are guaranteed to converge to correct posterior bounds. We also discuss calculation of bounds for expected utilities and variances, and global perturbation models. 1
IPE and L2U: Approximate algorithms for credal networks
 IN PROCEEDINGS OF THE SECOND STARTING AI RESEARCHER SYMPOSIUM
, 2004
"... ..."
Reasoning in Evidential Networks with Conditional Belief Functions
, 1994
"... In the existing evidential networks applicable to belief functions, the relations among the variables are always represented by joint belief functions on the product space of the involved variables. In this paper, we use conditional belief functions to represent such relations in the network and sho ..."
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Cited by 11 (0 self)
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In the existing evidential networks applicable to belief functions, the relations among the variables are always represented by joint belief functions on the product space of the involved variables. In this paper, we use conditional belief functions to represent such relations in the network and show some relations between these two kinds of representations. We also present a propagation algorithm for such networks. By analyzing the properties of some special networks with conditional belief functions, called the network with partial dependency, we show that the computation for reasoning can be simplified. 1. Introduction Networkbased approaches have been widely used for knowledge representation and reasoning with uncertainties. Bayesian networks [3] and valuationbased systems [7] are two of wellknown frameworks. Bayesian networks are implemented for the probabilistic inference, while Valuationbased systems can represent several uncertainty formalisms in a unified framework. Grap...
Inference in Credal Networks with BranchAndBound Algorithms
 IN INT. SYMP. ON IMPRECISE PROBABILITIES AND THEIR APPLICATIONS
, 2003
"... A credal network associates sets of probability distributions with directed acyclic graphs. Under strong independence assumptions, inference with credal networks is equivalent to a signomial program under linear constraints, a problem that is NPhard even for categorical variables and polytree mo ..."
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Cited by 11 (1 self)
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A credal network associates sets of probability distributions with directed acyclic graphs. Under strong independence assumptions, inference with credal networks is equivalent to a signomial program under linear constraints, a problem that is NPhard even for categorical variables and polytree models. We describe
Irrelevance and Independence Relations in QuasiBayesian Networks
 In Proceedings UAI98
, 1998
"... This paper analyzes irrelevance and independence relations in graphical models associated with convex sets of probability distributions (called QuasiBayesian networks). The basic question in QuasiBayesian networks is, How can irrelevance/independence relations in QuasiBayesian networks be d ..."
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Cited by 9 (2 self)
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This paper analyzes irrelevance and independence relations in graphical models associated with convex sets of probability distributions (called QuasiBayesian networks). The basic question in QuasiBayesian networks is, How can irrelevance/independence relations in QuasiBayesian networks be detected, enforced and exploited? This paper addresses these questions through Walley's definitions of irrelevance and independence. Novel algorithms and results are presented for inferences with the socalled natural extensions using fractional linear programming, and the properties of the socalled type1 extensions are clarified through a new generalization of dseparation. 1
Propositional and relational Bayesian networks associated with imprecise and qualitative probabilistic assessments
 IN PROCEEDINGS OF THE 20TH ANNUAL CONFERENCE ON UNCERTAINTY IN ARTIFICIAL INTELLIGENCE
, 2004
"... This paper investigates a representation language with flexibility inspired by probabilistic logic and compactness inspired by relational Bayesian networks. The goal is to handle propositional and firstorder constructs together with precise, imprecise, indeterminate and qualitative probabilistic as ..."
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Cited by 8 (4 self)
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This paper investigates a representation language with flexibility inspired by probabilistic logic and compactness inspired by relational Bayesian networks. The goal is to handle propositional and firstorder constructs together with precise, imprecise, indeterminate and qualitative probabilistic assessments. The paper shows how this can be achieved through the theory of credal networks. New exact and approximate inference algorithms based on multilinear programming and iterated/loopy propagation of interval probabilities are presented; their superior performance, compared to existing ones, is shown empirically.
Transferable belief Model for Decision Making in the ValuationBased Systems
 IEEE Trans. Systems, Man , and Cybernetics  A
, 1995
"... In this paper, we present a decision support system which is based on the transferable belief model(TBM), a model that quantifies someone's degree of belief using belief functions. The system performs evidential reasoning and decision making by integrating an evidential system for belief functi ..."
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Cited by 6 (0 self)
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In this paper, we present a decision support system which is based on the transferable belief model(TBM), a model that quantifies someone's degree of belief using belief functions. The system performs evidential reasoning and decision making by integrating an evidential system for belief function propagation and a valuationbased system for Bayesian decision analysis. The two subsystems are both within the framework of the valuationbased systems. They are connected through the pignistic transformation as described in the context of the TBM. The system takes as inputs the user's beliefs about a situation, and suggests what, if any, are to be tested and in which order. It does so with a userfriendly interface. An example concerning a nuclear waste disposal problem will be given to demonstrate an application of the system in a realworld domain. 1 Introduction Decision making under uncertainty is a common problem in the real world. Decision analysis provides a way to solve ...