Amen Ajroud | University of Sousse (original) (raw)
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Papers by Amen Ajroud
2011 Annual Meeting of the North American Fuzzy Information Processing Society, 2011
ABSTRACT
Product-Based Possibilistic Networks appear to be important tools to efficiently and compactly re... more Product-Based Possibilistic Networks appear to be important tools to efficiently and compactly represent possibility distributions. The inference process is a crucial task to propagate information into network when new pieces of information, called evidence, are observed. However, this inference process is known to be a hard task especially for multiply connected networks. In this paper, we propose an approximate algorithm for product-based possibilistic networks. More precisely, we propose an adaptation of the probabilistic approach "Loopy Belief Propagation" (LBP) for possibilistic networks.
Possibilistic networks are useful tools for reasoning under uncertainty. Uncertain pieces of info... more Possibilistic networks are useful tools for reasoning under uncertainty. Uncertain pieces of information can be described by different measures: possibility measures, necessity measures and more recently, guaranteed possibility measures, denoted by ∆. This paper first proposes the use of guaranteed possibility measures to define a so-called ∆-based possibilistic network. This graphical representation tries to express and to deal with the minimal (lower-bound) possibility degree guaranteed for each variable. We then establish relationships between graphical and logical-based representations of uncertain information encoded by guaranteed possibility measures. We show that possibilistic networks based on guaranteed possibility measures can be easily transformed, in a polynomial time, in ∆-based knowledge bases. Then we analyze propagation algorithms in ∆based possibilistic networks. In fact, standard possibilistic propagation algorithms can be re-used since we show that a simple rewriting of the chain rule allows the transformation of the initial ∆-based possibilistic networks into standard min-based possibilistic networks.
International Journal of Intelligent Systems, 2014
ABSTRACT
Editorial Board
We present a novel inference algorithm which is an adaptation of Loopy Belief Propagation applied... more We present a novel inference algorithm which is an adaptation of Loopy Belief Propagation applied on Product-Based Possibilistic Networks. Without any transformation of the initial graph, the basic idea of this adaptation is to propagate evidence into network by passing messages between nodes until a convergence state is reached (if ever). Product-Based Possibilistic Networks appear to be important tools to efficiently and compactly represent possibility distributions. This inference process is known to be a crucial and a hard task especially for multiply-connected networks i.e. with loops.
In this paper we present a synthesis of the work performed on two inference algorithms: the Pearl... more In this paper we present a synthesis of the work performed on two inference algorithms: the Pearl's belief propagation (BP) algorithm applied to Bayesian networks without loops (i.e. polytree) and the Loopy belief propagation (LBP) algorithm (inspired from the BP) which is applied to networks containing undirected cycles. It is known that the BP algorithm, applied to Bayesian networks with loops, gives incorrect numerical results i.e. incorrect posterior probabilities. Murphy and al. find that the LBP algorithm converges on several networks and when this occurs, LBP gives a good approximation of the exact posterior probabilities. However this algorithm presents an oscillatory behaviour when it is applied to QMR (Quick Medical Reference) network . This phenomenon prevents the LBP algorithm from converging towards a good approximation of posterior probabilities. We believe that the translation of the inference computation problem from the probabilistic framework to the possibilistic framework will allow performance improvement of LBP algorithm. We hope that an adaptation of this algorithm to a possibilistic causal network will show an improvement of the convergence of LBP.
Most artificial intelligence applications, especially expert systems, have to reason and make dec... more Most artificial intelligence applications, especially expert systems, have to reason and make decisions based on uncertain data and uncertain models. For this reason, several methods have been proposed for reasoning with different kinds of uncertainty. This paper discusses and illustrates some of the reasoning methods proposed by the artificial intelligence research community to deal with uncertainty.
2011 Annual Meeting of the North American Fuzzy Information Processing Society, 2011
ABSTRACT
Product-Based Possibilistic Networks appear to be important tools to efficiently and compactly re... more Product-Based Possibilistic Networks appear to be important tools to efficiently and compactly represent possibility distributions. The inference process is a crucial task to propagate information into network when new pieces of information, called evidence, are observed. However, this inference process is known to be a hard task especially for multiply connected networks. In this paper, we propose an approximate algorithm for product-based possibilistic networks. More precisely, we propose an adaptation of the probabilistic approach "Loopy Belief Propagation" (LBP) for possibilistic networks.
Possibilistic networks are useful tools for reasoning under uncertainty. Uncertain pieces of info... more Possibilistic networks are useful tools for reasoning under uncertainty. Uncertain pieces of information can be described by different measures: possibility measures, necessity measures and more recently, guaranteed possibility measures, denoted by ∆. This paper first proposes the use of guaranteed possibility measures to define a so-called ∆-based possibilistic network. This graphical representation tries to express and to deal with the minimal (lower-bound) possibility degree guaranteed for each variable. We then establish relationships between graphical and logical-based representations of uncertain information encoded by guaranteed possibility measures. We show that possibilistic networks based on guaranteed possibility measures can be easily transformed, in a polynomial time, in ∆-based knowledge bases. Then we analyze propagation algorithms in ∆based possibilistic networks. In fact, standard possibilistic propagation algorithms can be re-used since we show that a simple rewriting of the chain rule allows the transformation of the initial ∆-based possibilistic networks into standard min-based possibilistic networks.
International Journal of Intelligent Systems, 2014
ABSTRACT
Editorial Board
We present a novel inference algorithm which is an adaptation of Loopy Belief Propagation applied... more We present a novel inference algorithm which is an adaptation of Loopy Belief Propagation applied on Product-Based Possibilistic Networks. Without any transformation of the initial graph, the basic idea of this adaptation is to propagate evidence into network by passing messages between nodes until a convergence state is reached (if ever). Product-Based Possibilistic Networks appear to be important tools to efficiently and compactly represent possibility distributions. This inference process is known to be a crucial and a hard task especially for multiply-connected networks i.e. with loops.
In this paper we present a synthesis of the work performed on two inference algorithms: the Pearl... more In this paper we present a synthesis of the work performed on two inference algorithms: the Pearl's belief propagation (BP) algorithm applied to Bayesian networks without loops (i.e. polytree) and the Loopy belief propagation (LBP) algorithm (inspired from the BP) which is applied to networks containing undirected cycles. It is known that the BP algorithm, applied to Bayesian networks with loops, gives incorrect numerical results i.e. incorrect posterior probabilities. Murphy and al. find that the LBP algorithm converges on several networks and when this occurs, LBP gives a good approximation of the exact posterior probabilities. However this algorithm presents an oscillatory behaviour when it is applied to QMR (Quick Medical Reference) network . This phenomenon prevents the LBP algorithm from converging towards a good approximation of posterior probabilities. We believe that the translation of the inference computation problem from the probabilistic framework to the possibilistic framework will allow performance improvement of LBP algorithm. We hope that an adaptation of this algorithm to a possibilistic causal network will show an improvement of the convergence of LBP.
Most artificial intelligence applications, especially expert systems, have to reason and make dec... more Most artificial intelligence applications, especially expert systems, have to reason and make decisions based on uncertain data and uncertain models. For this reason, several methods have been proposed for reasoning with different kinds of uncertainty. This paper discusses and illustrates some of the reasoning methods proposed by the artificial intelligence research community to deal with uncertainty.