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33
Lifted firstorder probabilistic inference
 In Proceedings of IJCAI05, 19th International Joint Conference on Artificial Intelligence
, 2005
"... Most probabilistic inference algorithms are specified and processed on a propositional level. In the last decade, many proposals for algorithms accepting firstorder specifications have been presented, but in the inference stage they still operate on a mostly propositional representation level. [Poo ..."
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Cited by 88 (7 self)
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Most probabilistic inference algorithms are specified and processed on a propositional level. In the last decade, many proposals for algorithms accepting firstorder specifications have been presented, but in the inference stage they still operate on a mostly propositional representation level. [Poole, 2003] presented a method to perform inference directly on the firstorder level, but this method is limited to special cases. In this paper we present the first exact inference algorithm that operates directly on a firstorder level, and that can be applied to any firstorder model (specified in a language that generalizes undirected graphical models). Our experiments show superior performance in comparison with propositional exact inference. 1
Updating Beliefs with Incomplete Observations
"... Currently, there is renewed interest in the problem, raised by Shafer in 1985, of updating probabilities when observations are incomplete (or setvalued). This is a fundamental problem in general, and of particular interest for Bayesian networks. Recently, Gr unwald and Halpern have shown that co ..."
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Cited by 32 (10 self)
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Currently, there is renewed interest in the problem, raised by Shafer in 1985, of updating probabilities when observations are incomplete (or setvalued). This is a fundamental problem in general, and of particular interest for Bayesian networks. Recently, Gr unwald and Halpern have shown that commonly used updating strategies fail in this case, except under very special assumptions. In this paper we propose a new method for updating probabilities with incomplete observations. Our approach is deliberately conservative: we make no assumptions about the socalled incompleteness mechanism that associates complete with incomplete observations. We model our ignorance about this mechanism by a vacuous lower prevision, a tool from the theory of imprecise probabilities, and we use only coherence arguments to turn prior into posterior (updated) probabilities. In general, this new approach to updating produces lower and upper posterior probabilities and previsions (expectations), as well as partially determinate decisions. This is a logical consequence of the existing ignorance about the incompleteness mechanism. As an example, we use the new updating method to properly address the apparent paradox in the `Monty Hall' puzzle. More importantly, we apply it to the problem of classification of new evidence in probabilistic expert systems, where it leads to a new, socalled conservative updating rule.
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 28 (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
Decisiontheoretic specification of credal networks: a unified language for uncertain modeling with sets of Bayesian networks
 International Journal of Approximate Reasoning
"... Credal networks are models that extend Bayesian nets to deal with imprecision in probability, and can actually be regarded as sets of Bayesian nets. Credal nets appear to be powerful means to represent and deal with many important and challenging problems in uncertain reasoning. We give examples to ..."
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Cited by 15 (8 self)
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Credal networks are models that extend Bayesian nets to deal with imprecision in probability, and can actually be regarded as sets of Bayesian nets. Credal nets appear to be powerful means to represent and deal with many important and challenging problems in uncertain reasoning. We give examples to show that some of these problems can only be modeled by credal nets called nonseparately specified. These, however, are still missing a graphical representation language and updating algorithms. The situation is quite the opposite with separately specified credal nets, which have been the subject of much study and algorithmic development. This paper gives two major contributions. First, it delivers a new graphical language to formulate any type of credal network, both separately and nonseparately specified. Second, it shows that any nonseparately specified net represented with the new language can be easily transformed into an equivalent separately specified net, defined over a larger domain. This result opens up a number of new outlooks and concrete outcomes: first of all, it immediately enables the existing algorithms for separately specified credal nets to be applied to nonseparately specified ones. We explore this possibility for the 2U algorithm: an algorithm for exact updating of singly connected credal nets, which is extended by our results to a class of nonseparately specified models. We also consider the problem of inference on Bayesian networks, when the reason that prevents some of the variables from being observed is unknown. The problem is first reformulated in the new graphical language, and then mapped into an equivalent problem on a separately specified net. This provides a first algorithmic approach to this kind of inference, which is also proved to be NPhard by similar transformations based on our formalism.
IPE and L2U: Approximate algorithms for credal networks
 IN PROCEEDINGS OF THE SECOND STARTING AI RESEARCHER SYMPOSIUM
, 2004
"... ..."
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
Generalized Loopy 2U: A New Algorithm for Approximate Inference in Credal Networks
"... Credal nets generalize Bayesian nets by relaxing the requirement of precision of probabilities. Credal nets are considerably more expressive than Bayesian nets, but this makes belief updating NPhard even on polytrees. We develop a new efficient algorithm for approximate belief updating in credal ne ..."
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Cited by 11 (8 self)
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Credal nets generalize Bayesian nets by relaxing the requirement of precision of probabilities. Credal nets are considerably more expressive than Bayesian nets, but this makes belief updating NPhard even on polytrees. We develop a new efficient algorithm for approximate belief updating in credal nets. The algorithm is based on an important representation result we prove for general credal nets: that any credal net can be equivalently reformulated as a credal net with binary variables; moreover, the transformation, which is considerably more complex than in the Bayesian case, can be implemented in polynomial time. The equivalent binary credal net is updated by L2U, a loopy approximate algorithm for binary credal nets. Thus, we generalize L2U to nonbinary credal nets, obtaining an accurate and scalable algorithm for the general case, which is approximate only because of its loopy nature. The accuracy of the inferences is evaluated by empirical tests. 1
A Review of Propagation Algorithms for Imprecise Probabilities
, 1999
"... This paper reviews algorithms for local computation with imprecise probabilities. These algorithms try to solve problems of inference (calculation of conditional or unconditional probabilities) in cases in which there are a large number of variables. There are two main types depending on the nature ..."
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Cited by 11 (1 self)
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This paper reviews algorithms for local computation with imprecise probabilities. These algorithms try to solve problems of inference (calculation of conditional or unconditional probabilities) in cases in which there are a large number of variables. There are two main types depending on the nature of assumed independence relationships in each case. In both of them the global knowledge is composed of several pieces of local information. The objective is to carry out a sound global computation but mainly using the initial local representation. Keywords. Propagation algorithms, valuations based systems, imprecise probabilities. 1
Belief updating and learning in semiqualitative probabilistic networks
 Conference on Uncertainty in Artificial Intelligence. AUAI
, 2005
"... This paper explores semiqualitative probabilistic networks (SQPNs) that combine numeric and qualitative information. We first show that exact inferences with SQPNs are NP PPComplete. We then show that existing qualitative relations in SQPNs (plus probabilistic logic and imprecise assessments) can ..."
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Cited by 9 (5 self)
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This paper explores semiqualitative probabilistic networks (SQPNs) that combine numeric and qualitative information. We first show that exact inferences with SQPNs are NP PPComplete. We then show that existing qualitative relations in SQPNs (plus probabilistic logic and imprecise assessments) can be dealt effectively through multilinear programming. We then discuss learning: we consider a maximum likelihood method that generates point estimates given a SQPN and empirical data, and we describe a Bayesianminded method that employs the Imprecise Dirichlet Model to generate setvalued estimates. 1
Epistemic irrelevance in credal networks: the case of imprecise Markov trees
 IN ISIPTA ’09 – PROCEEDINGS OF THE SIXTH INTERNATIONAL SYMPOSIUM ON IMPRECISE PROBABILITY
, 2009
"... We replace strong independence in credal networks with the weaker notion of epistemic irrelevance. Focusing on directed trees, we show how to combine local credal sets into a global model, and we use this to construct and justify an exact messagepassing algorithm that computes updated beliefs for a ..."
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Cited by 9 (8 self)
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We replace strong independence in credal networks with the weaker notion of epistemic irrelevance. Focusing on directed trees, we show how to combine local credal sets into a global model, and we use this to construct and justify an exact messagepassing algorithm that computes updated beliefs for a variable in the tree. The algorithm, which is essentially linear in the number of nodes, is formulated entirely in terms of coherent lower previsions. We supply examples of the algorithm’s operation, and report an application to online character recognition that illustrates the advantages of our model for prediction.