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Destercke S.,CNRS Heuristic and Diagnostic Methods for Complex Systems
International Journal of Approximate Reasoning | Year: 2013

In imprecise probability theories, independence modeling and computational tractability are two important issues. The former is essential to work with multiple variables and multivariate spaces, while the latter is essential in practical applications. When using lower probabilities to model uncertainty about the value assumed by a variable, satisfying the property of 2-monotonicity decreases the computational burden of inference, hence answering the latter issue. In a first part, this paper investigates whether the joint uncertainty obtained by main existing notions of independence preserve the 2-monotonicity of marginal models. It is shown that it is usually not the case, except for the formal extension of random set independence to 2-monotone lower probabilities. The second part of the paper explores the properties and interests of this extension within the setting of lower probabilities. © 2012 Elsevier Inc. All.


Denoeux T.,CNRS Heuristic and Diagnostic Methods for Complex Systems
International Journal of Approximate Reasoning | Year: 2014

Given a parametric statistical model, evidential methods of statistical inference aim at constructing a belief function on the parameter space from observations. The two main approaches are Dempster's method, which regards the observed variable as a function of the parameter and an auxiliary variable with known probability distribution, and the likelihood-based approach, which considers the relative likelihood as the contour function of a consonant belief function. In this paper, we revisit the latter approach and prove that it can be derived from three basic principles: the likelihood principle, compatibility with Bayes' rule and the minimal commitment principle. We then show how this method can be extended to handle low-quality data. Two cases are considered: observations that are only partially relevant to the population of interest, and data acquired through an imperfect observation process. © 2013 Elsevier Inc.


Bechkit W.,CNRS Heuristic and Diagnostic Methods for Complex Systems | Challal Y.,CNRS Heuristic and Diagnostic Methods for Complex Systems | Bouabdallah A.,CNRS Heuristic and Diagnostic Methods for Complex Systems | Tarokh V.,Harvard University
IEEE Transactions on Wireless Communications | Year: 2013

Given the sensitivity of the potential WSN applications and because of resource limitations, key management emerges as a challenging issue for WSNs. One of the main concerns when designing a key management scheme is the network scalability. Indeed, the protocol should support a large number of nodes to enable a large scale deployment of the network. In this paper, we propose a new scalable key management scheme for WSNs which provides a good secure connectivity coverage. For this purpose, we make use of the unital design theory. We show that the basic mapping from unitals to key pre-distribution allows us to achieve high network scalability. Nonetheless, this naive mapping does not guarantee a high key sharing probability. Therefore, we propose an enhanced unital-based key pre-distribution scheme providing high network scalability and good key sharing probability approximately lower bounded by 1-e{-1} ≈ 0.632. We conduct approximate analysis and simulations and compare our solution to those of existing methods for different criteria such as storage overhead, network scalability, network connectivity, average secure path length and network resiliency. Our results show that the proposed approach enhances the network scalability while providing high secure connectivity coverage and overall improved performance. Moreover, for an equal network size, our solution reduces significantly the storage overhead compared to those of existing solutions. © 2012 IEEE.


Denoeux T.,CNRS Heuristic and Diagnostic Methods for Complex Systems
IEEE Transactions on Knowledge and Data Engineering | Year: 2013

We consider the problem of parameter estimation in statistical models in the case where data are uncertain and represented as belief functions. The proposed method is based on the maximization of a generalized likelihood criterion, which can be interpreted as a degree of agreement between the statistical model and the uncertain observations. We propose a variant of the EM algorithm that iteratively maximizes this criterion. As an illustration, the method is applied to uncertain data clustering using finite mixture models, in the cases of categorical and continuous attributes. © 1989-2012 IEEE.


Denoeux T.,CNRS Heuristic and Diagnostic Methods for Complex Systems
International Journal of Approximate Reasoning | Year: 2014

This note is a rejoinder to comments by Dubois and Moral about my paper "Likelihood-based belief function: justification and some extensions to low-quality data" published in this issue. The main comments concern (1) the axiomatic justification for defining a consonant belief function in the parameter space from the likelihood function and (2) the Bayesian treatment of statistical inference from uncertain observations, when uncertainty is quantified by belief functions. Both issues are discussed in this note, in response to the discussants' comments. © 2014 Elsevier Inc.


Destercke S.,CNRS Heuristic and Diagnostic Methods for Complex Systems
International Journal of Approximate Reasoning | Year: 2014

This paper is a fine review of various aspects related to the statistical handling of "ontic" random fuzzy sets by the means of appropriate distances. It is quite comprehensive and helpful, as it clarifies the status of fuzzy sets in such methods, explains the advantages of using a distance-based approach, specifies the pitfalls in which one should not fall when dealing with "ontic" random fuzzy sets and provides some illustration of practical computations. Not being a statistician but an occasional user of statistics, my discussion will mainly focus on this more practical aspect. © 2014 Elsevier Inc.


Destercke S.,CNRS Heuristic and Diagnostic Methods for Complex Systems
International Journal of Approximate Reasoning | Year: 2014

Eyke Hüllermeier provides a very convincing approach to learn from fuzzy data, both about the model and about the data themselves. In the process, he links the shape of fuzzy sets with classical loss functions, therefore providing strong theoretical links between fuzzy modeling and more classical machine learning approaches. This short note discusses various aspects of his proposal as well as possible extensions. I will first discuss the opportunity to consider more general uncertainty representations, before considering various alternatives to the proposed learning procedure. Finally, I will briefly discuss the differences I perceive about a loss-based and a likelihood-based approach. © 2014 Elsevier Inc.


Kanjanatarakul O.,Chiang Mai Rajabhat University | Sriboonchitta S.,Chiang Mai University | Denoeux T.,CNRS Heuristic and Diagnostic Methods for Complex Systems
International Journal of Approximate Reasoning | Year: 2014

A method is proposed to quantify uncertainty on statistical forecasts using the formalism of belief functions. The approach is based on two steps. In the estimation step, a belief function on the parameter space is constructed from the normalized likelihood given the observed data. In the prediction step, the variable Y to be forecasted is written as a function of the parameter θ and an auxiliary random variable Z with known distribution not depending on the parameter, a model initially proposed by Dempster for statistical inference. Propagating beliefs about θ and Z through this model yields a predictive belief function on Y. The method is demonstrated on the problem of forecasting innovation diffusion using the Bass model, yielding a belief function on the number of adopters of an innovation in some future time period, based on past adoption data. © 2014 Elsevier B.V. All rights reserved.


Ben Abdallah N.,CNRS Heuristic and Diagnostic Methods for Complex Systems | Mouhous-Voyneau N.,CNRS Urban Systems Engineering | Denoeux T.,CNRS Heuristic and Diagnostic Methods for Complex Systems
International Journal of Approximate Reasoning | Year: 2014

Estimation of extreme sea levels for high return periods is of prime importance in hydrological design and flood risk assessment. Common practice consists of inferring design levels from historical observations and assuming the distribution of extreme values to be stationary. However, in recent years, there has been a growing awareness of the necessity to integrate the effects of climate change in environmental analysis. In this paper, we present a methodology based on belief functions to combine statistical judgements with expert evidence in order to predict the future centennial sea level at a particular location, taking into account climate change. Likelihood-based belief functions derived from statistical observations are combined with random intervals encoding expert assessments of the 21st century sea level rise. Monte Carlo simulations allow us to compute belief and plausibility degrees for various hypotheses about the design parameter. © 2013 Elsevier Inc. All rights reserved.


Rault T.,CNRS Heuristic and Diagnostic Methods for Complex Systems | Bouabdallah A.,CNRS Heuristic and Diagnostic Methods for Complex Systems | Challal Y.,CNRS Heuristic and Diagnostic Methods for Complex Systems
Computer Networks | Year: 2014

The design of sustainable wireless sensor networks (WSNs) is a very challenging issue. On the one hand, energy-constrained sensors are expected to run autonomously for long periods. However, it may be cost-prohibitive to replace exhausted batteries or even impossible in hostile environments. On the other hand, unlike other networks, WSNs are designed for specific applications which range from small-size healthcare surveillance systems to large-scale environmental monitoring. Thus, any WSN deployment has to satisfy a set of requirements that differs from one application to another. In this context, a host of research work has been conducted in order to propose a wide range of solutions to the energy-saving problem. This research covers several areas going from physical layer optimisation to network layer solutions. Therefore, it is not easy for the WSN designer to select the efficient solutions that should be considered in the design of application-specific WSN architecture. We present a top-down survey of the trade-offs between application requirements and lifetime extension that arise when designing wireless sensor networks. We first identify the main categories of applications and their specific requirements. Then we present a new classification of energy-conservation schemes found in the recent literature, followed by a systematic discussion as to how these schemes conflict with the specific requirements. Finally, we survey the techniques applied in WSNs to achieve trade-off between multiple requirements, such as multi-objective optimisation. © 2014 Elsevier B.V. All rights reserved.

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