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Title:

Probabilistic-possibilistic belief networks

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The interpretation of membership functions of fuzzy sets as statistical likelihood functions leads to a probabilistic-possibilistic hierarchical description of uncertain knowledge. The fundamental advantage of the resulting fuzzy probabilities with respect to imprecise probabilities is the ability of using all the information provided by the dat...

The interpretation of membership functions of fuzzy sets as statistical likelihood functions leads to a probabilistic-possibilistic hierarchical description of uncertain knowledge. The fundamental advantage of the resulting fuzzy probabilities with respect to imprecise probabilities is the ability of using all the information provided by the data. This paper studies the possibility of using fuzzy probabilities to describe the uncertain knowledge about the values of the nodes of belief networks. 1 Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-08-18

Source:

http://epub.ub.uni-muenchen.de/4448/1/report.pdf

http://epub.ub.uni-muenchen.de/4448/1/report.pdf Minimize

Document Type:

text

Language:

en

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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http://www.stat.uni-muenchen.de Probabilistic-Possibilistic Belief Networks

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The interpretation of membership functions of fuzzy sets as statistical likelihood functions leads to a probabilistic-possibilistic hierarchical description of uncertain knowledge. The fundamental advantage of the resulting fuzzy probabilities with respect to imprecise probabilities is the ability of using all the information provided by the dat...

The interpretation of membership functions of fuzzy sets as statistical likelihood functions leads to a probabilistic-possibilistic hierarchical description of uncertain knowledge. The fundamental advantage of the resulting fuzzy probabilities with respect to imprecise probabilities is the ability of using all the information provided by the data. This paper studies the possibility of using fuzzy probabilities to describe the uncertain knowledge about the values of the nodes of belief networks. 1 Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2010-09-24

Source:

http://www.stat.uni-muenchen.de/%7Ecattaneo/publications/lmu32.pdf

http://www.stat.uni-muenchen.de/%7Ecattaneo/publications/lmu32.pdf Minimize

Document Type:

text

Language:

en

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

Likelihood-based inference for probabilistic graphical models: Some preliminary results

Description:

A method for calculating some profile likelihood inferences in probabilistic graphical models is presented and applied to the problem of classification. It can also be interpreted as a method for obtaining inferences from hierarchical networks, a kind of imprecise probabilistic graphical models. 1

A method for calculating some profile likelihood inferences in probabilistic graphical models is presented and applied to the problem of classification. It can also be interpreted as a method for obtaining inferences from hierarchical networks, a kind of imprecise probabilistic graphical models. 1 Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2011-05-08

Source:

http://www.stat.uni-muenchen.de/%7Ecattaneo/publications/pgm10.pdf

http://www.stat.uni-muenchen.de/%7Ecattaneo/publications/pgm10.pdf Minimize

Document Type:

text

Language:

en

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

Belief functions combination without the assumption of independence of the information sources

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-09-13

Source:

http://www.stat.uni-muenchen.de/~cattaneo/publications/ijar1-uv.pdf

http://www.stat.uni-muenchen.de/~cattaneo/publications/ijar1-uv.pdf Minimize

Document Type:

text

Language:

en

Subjects:

Key words ; Dempster-Shafer theory ; belief functions ; combination rule ; dependence ; conflict ; cautious combination

Key words ; Dempster-Shafer theory ; belief functions ; combination rule ; dependence ; conflict ; cautious combination Minimize

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Title:

7th International Symposium on Imprecise Probability: Theories and Applications, Innsbruck, Austria, 2011 Likelihood-Based Naive Credal Classifier

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The naive credal classifier extends the classical naive Bayes classifier to imprecise probabilities, substituting the imprecise Dirichlet model for the uniform prior. As an alternative to the naive credal classifier, we present a likelihood-based approach, which extends in a novel way the naive Bayes towards imprecise probabilities, by consideri...

The naive credal classifier extends the classical naive Bayes classifier to imprecise probabilities, substituting the imprecise Dirichlet model for the uniform prior. As an alternative to the naive credal classifier, we present a likelihood-based approach, which extends in a novel way the naive Bayes towards imprecise probabilities, by considering any possible quantification (each one defining a naive Bayes classifier) apart from those assigning to the available data a probability below a given threshold level. Besides the available supervised data, in the likelihood evaluation we also consider the instance to be classified, for which the value of the class variable is assumed missingat-random. We obtain a closed formula to compute the dominance according to the maximality criterion for any threshold level. As there are currently no well-established metrics for comparing credal classifiers which have considerably different determinacy, we compare the two classifiers when they have comparable determinacy, finding that in those cases they generate almost equivalent classifications. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-05-30

Source:

http://www.stat.uni-muenchen.de/%7Ecattaneo/publications/isipta11-1.pdf

http://www.stat.uni-muenchen.de/%7Ecattaneo/publications/isipta11-1.pdf Minimize

Document Type:

text

Language:

en

Subjects:

naive credal classifier

naive credal classifier Minimize

DDC:

519 Probabilities & applied mathematics *(computed)*

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Title:

Likelihood-based inference for probabilistic graphical models: Some preliminary results

Description:

A method for calculating some profile likelihood inferences in probabilistic graphical models is presented and applied to the problem of classification. It can also be interpreted as a method for obtaining inferences from hierarchical networks, a kind of imprecise probabilistic graphical models. 1

A method for calculating some profile likelihood inferences in probabilistic graphical models is presented and applied to the problem of classification. It can also be interpreted as a method for obtaining inferences from hierarchical networks, a kind of imprecise probabilistic graphical models. 1 Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2010-09-29

Source:

http://www.helsinki.fi/pgm2010/papers/cattaneo.pdf

http://www.helsinki.fi/pgm2010/papers/cattaneo.pdf Minimize

Document Type:

text

Language:

en

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Title:

Probabilistic-possibilistic belief networks

Description:

Abstract: The interpretation of membership functions of fuzzy sets as statistical likelihood functions leads to a probabilistic-possibilistic hierarchical description of uncertain knowledge. The fundamental advantage of the resulting fuzzy probabilities with respect to imprecise probabilities is the ability of using all the information provided ...

Abstract: The interpretation of membership functions of fuzzy sets as statistical likelihood functions leads to a probabilistic-possibilistic hierarchical description of uncertain knowledge. The fundamental advantage of the resulting fuzzy probabilities with respect to imprecise probabilities is the ability of using all the information provided by the data. This paper studies the possibility of using fuzzy probabilities to describe the uncertain knowledge about the values of the nodes of belief networks. 1 Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2011-05-08

Source:

http://www.stat.uni-muenchen.de/%7Ecattaneo/publications/vsim09.pdf

http://www.stat.uni-muenchen.de/%7Ecattaneo/publications/vsim09.pdf Minimize

Document Type:

text

Language:

en

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

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7th International Symposium on Imprecise Probability: Theories and Applications, Innsbruck, Austria, 2011 Regression with Imprecise Data: A Robust Approach

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We introduce a robust regression method for imprecise data, and apply it to social survey data. Our method combines nonparametric likelihood inference with imprecise probability, so that only very weak assumptions are needed and different kinds of uncertainty can be taken into account. The proposed regression method is based on interval dominanc...

We introduce a robust regression method for imprecise data, and apply it to social survey data. Our method combines nonparametric likelihood inference with imprecise probability, so that only very weak assumptions are needed and different kinds of uncertainty can be taken into account. The proposed regression method is based on interval dominance: interval estimates of quantiles of the error distribution are used to identify plausible descriptions of the relationship of interest. In the application to social survey data, the resulting set of plausible descriptions is relatively large, reflecting the amount of uncertainty inherent in the analyzed data set. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-05-25

Source:

http://www.stat.uni-muenchen.de/%7Ecattaneo/publications/isipta11-2.pdf

http://www.stat.uni-muenchen.de/%7Ecattaneo/publications/isipta11-2.pdf Minimize

Document Type:

text

Language:

en

Subjects:

imprecise data

imprecise data Minimize

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Title:

Likelihood-Based Robust Classification with Bayesian Networks

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Abstract. Bayesian networks are commonly used for classification: a structural learning algorithm determines the network graph, while standard approaches estimate the model parameters from data. Yet, with few data the corresponding assessments can be unreliable. To gain robustness in this phase, we consider a likelihood-based learning approach, ...

Abstract. Bayesian networks are commonly used for classification: a structural learning algorithm determines the network graph, while standard approaches estimate the model parameters from data. Yet, with few data the corresponding assessments can be unreliable. To gain robustness in this phase, we consider a likelihood-based learning approach, which takes all the model quantifications whose likelihood exceeds a given threshold. A new classification algorithm based on this approach is presented. Notably, this is a credal classifier, i.e., more than a single class can be returned in output. This is the case when the Bayesian networks consistent with the threshold constraint assign different class labels to a test instance. This is the first classifier of this kind for general topologies. Experiments show how this approach provide the desired robustness. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-07-17

Source:

http://www.stat.uni-muenchen.de/~cattaneo/publications/ipmu12-uv.pdf

http://www.stat.uni-muenchen.de/~cattaneo/publications/ipmu12-uv.pdf Minimize

Document Type:

text

Language:

en

Subjects:

Classification ; likelihood-based learning ; Bayesian networks ; credal networks

Classification ; likelihood-based learning ; Bayesian networks ; credal networks Minimize

DDC:

006 Special computer methods *(computed)*

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Title:

Fuzzy probabilities based on the likelihood function. In Soft Methods for Handling Variability and Imprecision

Description:

Abstract. If we interpret the statistical likelihood function as a measure of the relative plausibility of the probabilistic models considered, then we obtain a hierarchical description of uncertain knowledge, offering a unified approach to the combination of probabilistic and possibilistic uncertainty. The fundamental advantage of the resulting...

Abstract. If we interpret the statistical likelihood function as a measure of the relative plausibility of the probabilistic models considered, then we obtain a hierarchical description of uncertain knowledge, offering a unified approach to the combination of probabilistic and possibilistic uncertainty. The fundamental advantage of the resulting fuzzy probabilities with respect to imprecise probabilities is the ability of using all the information provided by the data. Minimize

Publisher:

Springer

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2010-09-24

Source:

http://www.stat.uni-muenchen.de/%7Ecattaneo/publications/smps08.pdf

http://www.stat.uni-muenchen.de/%7Ecattaneo/publications/smps08.pdf Minimize

Document Type:

text

Language:

en

Subjects:

Likelihood function ; Hierarchical model ; Fuzzy probabilities ; Imprecise probabilities ; Statistical inconsistency

Likelihood function ; Hierarchical model ; Fuzzy probabilities ; Imprecise probabilities ; Statistical inconsistency Minimize

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