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Probabilistic logic and probabilistic networks
, 2008
"... While in principle probabilistic logics might be applied to solve a range of problems, in practice they are rarely applied at present. This is perhaps because they seem disparate, complicated, and computationally intractable. However, we shall argue in this programmatic paper that several approaches ..."
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While in principle probabilistic logics might be applied to solve a range of problems, in practice they are rarely applied at present. This is perhaps because they seem disparate, complicated, and computationally intractable. However, we shall argue in this programmatic paper that several approaches to probabilistic logic fit into a simple unifying framework: logically complex evidence can be used to associate probability intervals or probabilities with sentences. Specifically, we show in Part I that there is a natural way to present a question posed in probabilistic logic, and that various inferential procedures provide semantics for that question: the standard probabilistic semantics (which takes probability functions as models), probabilistic argumentation (which considers the probability of a hypothesis being a logical consequence of the available evidence), evidential probability (which handles reference classes and frequency data), classical statistical inference
Bayesian Networks with Imprecise Probabilities: Theory and Application to Classification
, 2010
"... Bayesian network are powerful probabilistic graphical models for modelling uncertainty. Among others, classification represents an important application: some of the most used classifiers are based on Bayesian networks. Bayesian networks are precise models: exact numeric values should be provided fo ..."
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Cited by 5 (2 self)
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Bayesian network are powerful probabilistic graphical models for modelling uncertainty. Among others, classification represents an important application: some of the most used classifiers are based on Bayesian networks. Bayesian networks are precise models: exact numeric values should be provided for quantification. This requirement is sometimes too narrow. Sets instead of single distributions can provide a more realistic description in these cases. Bayesian networks can be generalized to cope with sets of distributions. This leads to a novel class of imprecise probabilistic graphical models, called credal networks. In particular, classifiers based on Bayesian networks are generalized to socalled credal classifiers. Unlike Bayesian classifiers, which always detect a single class as the one maximizing the posterior class probability, a credal classifier may eventually be unable to discriminate a single class. In other words, if the available information is not sufficient, credal classifiers allow for indecision between two or more classes, this providing a less informative but more robust conclusion than Bayesian classifiers.
Credal nets with probabilities estimated with an extreme imprecise dirichlet model
 PROCEEDINGS OF THE FIFTH INTERNATIONAL SYMPOSIUM ON IMPRECISE PROBABILITY: THEORIES AND APPLICATIONS (ISIPTA ’07), ACTION M AGENCY
, 2007
"... The propagation of probabilities in credal networks when probabilities are estimated with a global imprecise Dirichlet model is an important open problem. Only Zaffalon [21] has proposed an algorithm for the Naive classifier. The main difficulty is that, in general, computing upper and lower probabi ..."
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Cited by 4 (0 self)
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The propagation of probabilities in credal networks when probabilities are estimated with a global imprecise Dirichlet model is an important open problem. Only Zaffalon [21] has proposed an algorithm for the Naive classifier. The main difficulty is that, in general, computing upper and lower probability intervals implies the resolution of an optimization of a fraction of two polynomials. In the case of the Naive credal classifier, Zaffalon has shown that the function is a convex function of only one parameter, but there is not a similar result for general credal sets. In this paper, we propose the use of an imprecise global model, but we restrict the distributions to only the most extreme ones. The result is a model giving rise that in the case of estimating a conditional probability under independence relationships, it can produce smaller intervals than the global general model. Its main advantage is that the optimization problem is simpler, and available procedures can be directly applied, as the ones proposed in [7].
Climbing the Hills of Compiled Credal Networks
 5TH INTERNATIONAL SYMPOSIUM ON IMPRECISE PROBABILITY: THEORIES AND APPLICATIONS, PRAGUE, CZECH REPUBLIC
, 2007
"... This paper introduces a new approximate inference algorithm for credal networks. The algorithm consists of two major steps. It starts by representing the credal network as a compiled logical theory. The resulting graphical structure is the basis on which the subsequent steepestascent hillclimbing ..."
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This paper introduces a new approximate inference algorithm for credal networks. The algorithm consists of two major steps. It starts by representing the credal network as a compiled logical theory. The resulting graphical structure is the basis on which the subsequent steepestascent hillclimbing algorithm operates. The output of the algorithm is an inner approximation of the exact lower and upper posterior probabilities.
Probabilistic Logic with Strong Independence
"... Abstract. This papers investigates the manipulation of statements of strong independence in probabilistic logic. Inference methods based on polynomial programming are presented for strong independence, both for unconditional and conditional cases. We also consider graphtheoretic representations, wh ..."
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Abstract. This papers investigates the manipulation of statements of strong independence in probabilistic logic. Inference methods based on polynomial programming are presented for strong independence, both for unconditional and conditional cases. We also consider graphtheoretic representations, where each node in a graph is associated with a Boolean variable and edges carry a Markov condition. The resulting model generalizes Bayesian networks, allowing probabilistic assessments and logical constraints to be mixed. 1
IDS: A DivideandConquer Algorithm for Inference in PolytreeShaped Credal Networks
"... Abstract. A credal network is a graphtheoretic model that represents imprecision in joint probability distributions. An inference in a credal net aims at computing an interval for the probability of an event of interest. Algorithms for inference in credal networks can be divided into exact and appr ..."
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Abstract. A credal network is a graphtheoretic model that represents imprecision in joint probability distributions. An inference in a credal net aims at computing an interval for the probability of an event of interest. Algorithms for inference in credal networks can be divided into exact and approximate. The selection of an algorithm is based on a trade off that ponders how much time someone wants to spend in a particular calculation against the quality of the computed values. This paper presents an algorithm, called IDS, that combines exact and approximate methods for computing inferences in polytreeshaped credal networks. The algorithm provides an approach to trade time and precision when making inferences in credal nets. Resumo. Uma rede credal é um formalismo baseado em grafos que representa imprecisão em distribuições conjuntas. Uma inferência em uma rede credal objetiva o cômputo de um intervalo de probabilidades para um evento de interesse. Os algoritmos para inferência em redes credais podem ser classificados como exatos ou aproximados. A seleção de um algoritmo exige uma análise de custo×benefício que pondera quanto tempo se deseja gastar no cálculo de um intervalo em relação a qualidade das aproximações. Este artigo apresenta um algoritmo, chamado IDS, que combina métodos exatos e aproximados no cômputo de inferências em redes com topologia em polytree e que provê uma estratégia para limitar o esforço computacional empregado em uma inferência. 1.
Local Computation in Credal Networks
"... Abstract. The goal of this contribution is to discuss local computation in credal networks — graphical models that can represent imprecise and indeterminate probability values. We analyze the inference problem in credal networks, discuss how inference algorithms can benefit from local computation, a ..."
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Abstract. The goal of this contribution is to discuss local computation in credal networks — graphical models that can represent imprecise and indeterminate probability values. We analyze the inference problem in credal networks, discuss how inference algorithms can benefit from local computation, and suggest that local computation can be particularly important in approximate inference algorithms. 1
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"... Application of a hillclimbing algorithm to exact and approximate ..."
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Probabilistic Graphical Models in Artificial Intelligence Abstract
"... In this paper, we review the role of probabilistic graphical models in artificial intelligence. We start by giving an account of the early years when there was important controversy about the suitability of probability for intelligent systems. We then discuss the main milestones for the foundations ..."
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In this paper, we review the role of probabilistic graphical models in artificial intelligence. We start by giving an account of the early years when there was important controversy about the suitability of probability for intelligent systems. We then discuss the main milestones for the foundations of graphical models starting with Pearl’s pioneering work. Some of the main techniques for problem solving (abduction, classification, and decision making) are briefly explained. Finally, we propose some important challenges for future research and highlight relevant applications (forensic reasoning, genomics and the use of graphical models as a general optimization tool).