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Decision-theoretic specification of credal networks: A unified language for uncertain modeling with sets of Bayesian networks

Alessandro Antonucci, Marco Zaffalon
2008 International Journal of Approximate Reasoning  
First, it delivers a new graphical language to formulate any type of credal network, both separately and non-separately specified.  ...  Credal networks are models that extend Bayesian nets to deal with imprecision in probability, and can actually be regarded as sets of Bayesian nets.  ...  First, we define a unified graphical language to locally specify credal networks in the general case (Section 6).  ... 
doi:10.1016/j.ijar.2008.02.005 fatcat:7sajtcscwbhwbo24vljn6czxpm

Inference with Seperately Specified Sets of Probabilities in Credal Networks [article]

Jose Carlos Ferreira da Rocha, Fabio Gagliardi Cozman
2012 arXiv   pre-print
Credal networks are here interpreted as encoding strong independence relations among variables. We first present a theory of credal networks based on separately specified sets of probabilities.  ...  We present new algorithms for inference in credal networks --- directed acyclic graphs associated with sets of probabilities.  ...  Suppose that all variables have three values and that every local credal set has only three vertices. The number of possible combi nations of vertices of local credal sets is 33 0 .  ... 
arXiv:1301.0597v1 fatcat:e37mylrfpze2xiiycc4oiucv4a

Graphical models for imprecise probabilities

Fabio Gagliardi Cozman
2005 International Journal of Approximate Reasoning  
The main characteristics of the credal network model are then discussed, as this model has received considerable attention in the literature.  ...  Andersen and Hooker have discussed credal networks that combine local and non-local credal sets [2] ; the discussion here is restricted to networks containing only local sets.  ...  Given a credal network with local separately specified credal sets K(X i jpa(X i )), the strong extension of the network is the convex hull of the set containing all joint distributions that factorize  ... 
doi:10.1016/j.ijar.2004.10.003 fatcat:icz32fuck5a65a26ndt5y4ooly

Inference in Polytrees with Sets of Probabilities [article]

Jose Carlos Ferreira da Rocha, Fabio Gagliardi Cozman, Cassio Polpo de Campos
2012 arXiv   pre-print
In this paper we focus on such inferences, and propose: 1) a substantial improvement on Tessems A / R algorithm FOR polytrees WITH probability intervals; 2) a new algorithm FOR direction - based local  ...  Acknowledgements We thank Jaime Ide for generating random networks that were used in our tests.  ...  In this paper we assume that local credal sets are always separately specified.  ... 
arXiv:1212.2458v1 fatcat:u24tty6jdrgkrhhouxynjmktre

Probabilistic Inference in Credal Networks: New Complexity Results

D. D. Maua, C. P. De Campos, A. Benavoli, A. Antonucci
2014 The Journal of Artificial Intelligence Research  
Credal networks are graph-based statistical models whose parameters take values in a set, instead of being sharply specified as in traditional statistical models (e.g., Bayesian networks).  ...  We prove that under epistemic irrelevance the polynomial-time complexity of inferences in credal trees is not likely to extend to more general models (e.g., singly connected topologies).  ...  The local credal sets are A node i in the network and its associated variable X i are said to be precise (i.e., precisely specified) if the corresponding conditional credal sets Q(X i |x Pa(i) ) are all  ... 
doi:10.1613/jair.4355 fatcat:j3kpexlnnze5ngdtpqilftl5ee

On the complexity of propositional and relational credal networks

Fabio Gagliardi Cozman, Denis Deratani Mauá
2017 International Journal of Approximate Reasoning  
Here we examine the complexity of inference in Boolean credal networks when probability measures are specified through formal languages, by extending a framework we have recently proposed for Bayesian  ...  In short, we explore the relationship between language and complexity in credal networks.  ...  This encodes the desired local, separately specified, credal sets.  ... 
doi:10.1016/j.ijar.2016.10.008 fatcat:a6ug55v2xzas5m3omnj4ygtj2u

Bayesian Networks with Imprecise Probabilities: Theory and Application to Classification [chapter]

G. Corani, A. Antonucci, M. Zaffalon
2012 Intelligent Systems Reference Library  
In particular, classifiers based on Bayesian networks are generalized to so-called credal classifiers.  ...  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.  ...  Note that this credal network is separately specified.  ... 
doi:10.1007/978-3-642-23166-7_4 fatcat:x7ep6izsujdm7ltfdq7p5saeo4

On the Complexity of Strong and Epistemic Credal Networks [article]

Denis D. Maua, Cassio Polpo de Campos, Alessio Benavoli, Alessandro Antonucci
2013 arXiv   pre-print
Credal networks are graph-based statistical models whose parameters take values in a set, instead of being sharply specified as in traditional statistical models (e.g., Bayesian networks).  ...  We prove that under epistemic irrelevance the polynomial time complexity of inferences in credal trees is not likely to extend to more general models (e.g. singly connected networks).  ...  When every local credal set is a singleton the model specifies a Bayesian network. Example 1. Consider the credal network N over Boolean variables X 1 , X 2 , X 3 whose graph is shown in Figure 1 .  ... 
arXiv:1309.6845v1 fatcat:p5ul4e5odvcyjfwbpwrcwcf75m

Inference in credal networks: branch-and-bound methods and the A/R+ algorithm

José Carlos Ferreira da Rocha, Fabio Gagliardi Cozman
2005 International Journal of Approximate Reasoning  
A credal network is a graphical representation for a set of joint probability distributions. In this paper we discuss algorithms for exact and approximate inferences in credal networks.  ...  We also propose a new algorithm, A/R+, for outer approximations in polytree-shaped credal networks.  ...  When intervals are locally transformed into credal sets, the optimization problems manipulating these credal sets produce the tightest possible bounds; however they start from larger feasible sets and  ... 
doi:10.1016/j.ijar.2004.10.009 fatcat:xeulvzqdtbdk3i6rwsnl23fqxe

Approximate credal network updating by linear programming with applications to decision making

Alessandro Antonucci, Cassio P. de Campos, David Huber, Marco Zaffalon
2015 International Journal of Approximate Reasoning  
Credal nets are probabilistic graphical models which extend Bayesian nets to cope with sets of distributions. An algorithm for approximate credal network updating is presented.  ...  A transformation is also derived to reduce decision making in credal networks based on the maximality criterion to updating.  ...  Before commenting on the results, note that our approach assumes the local credal sets to be specified by linear constraints.  ... 
doi:10.1016/j.ijar.2014.10.003 fatcat:b4xokgxxvjdwrju5tzf6ogar6u

Credal Networks under Maximum Entropy [article]

Thomas Lukasiewicz
2013 arXiv   pre-print
We apply the principle of maximum entropy to select a unique joint probability distribution from the set of all joint probability distributions specified by a credal network.  ...  Moreover, we apply the new principle of sequential maximum entropy to interval Bayesian networks and more generally to credal networks.  ...  Bayesian net works with local convex sets of conditional distributions, called credal networks (or also Quasi-Bayesian networks), are especially analyzed by Cozman [7, 8] .  ... 
arXiv:1301.3873v1 fatcat:uqyuzgb53zfvpeuuww6k5y7cby

Propositional and Relational Bayesian Networks Associated with Imprecise and Qualitative Probabilistic Assesments [article]

Fabio Gagliardi Cozman, Cassio Polpo de Campos, Jaime Ide, Jose Carlos Ferreira da Rocha
2012 arXiv   pre-print
The paper shows how this can be achieved through the theory of credal networks.  ...  This paper investigates a representation language with flexibility inspired by probabilistic logic and compactness inspired by relational Bayesian networks.  ...  into a network with polytree topology and separately specified credal sets, then inference is polynomial.  ... 
arXiv:1207.4121v1 fatcat:jw2kwnvjirbrpduat6tmstmxm4

Approximating Credal Network Inferences by Linear Programming [chapter]

Alessandro Antonucci, Cassio P. de Campos, David Huber, Marco Zaffalon
2013 Lecture Notes in Computer Science  
An algorithm for approximate credal network updating is presented.  ...  The approach can also be specialized to classification with credal networks based on the maximality criterion.  ...  Before commenting on the results in Tab. 1, note that our approach assumes the local credal sets to be specified by linear constraints.  ... 
doi:10.1007/978-3-642-39091-3_2 fatcat:u4jlzvcx7rdgfojkwkyhu2y7zm

Irrelevance and Independence Relations in Quasi-Bayesian Networks [article]

Fabio Gagliardi Cozman
2013 arXiv   pre-print
The basic question in Quasi-Bayesian networks is, How can irrelevance/independence relations in Quasi-Bayesian networks be detected, enforced and exploited?  ...  This paper analyzes irrelevance and independence relations in graphical models associated with convex sets of probability distributions (called Quasi-Bayesian networks).  ...  The difficulty is that neither of these credal sets is directly specified on the network; there is no simple constraint that ties them together.  ... 
arXiv:1301.7368v1 fatcat:xs6w5fabjvh3xiifwuhwh6u4bm

Assessing Debris Flow Hazard by Credal Nets [chapter]

Alessandro Antonucci, Andrea Salvetti, Marco Zaffalon
2004 Soft Methodology and Random Information Systems  
Credal networks [5] are impreciseprobability models based on the extension of Bayesian networks [9] to sets of probability mass functions (see Sec. 2.2).  ...  This paper presents a credal network model of debris flow hazard for the Ticino canton, southern Switzerland.  ...  This is actually done locally, by specifying the probabilistic relationship between a node and its parents.  ... 
doi:10.1007/978-3-540-44465-7_14 fatcat:es3sepqnfngx7jywwyfav62hje
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