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  • An expectation operator for belief functions in the Dempster–Shafer theory* * Presented at the 11th Workshop on Uncertainty Processing (WUPES'18), Třeboň, Czech Republic, June 6–9, 2018.View all notes
    Int. J. Gen. Syst. (IF 2.259) Pub Date : 2019-09-02
    Prakash P. Shenoy

    The main contribution of this paper is a new definition of expected value of belief functions in the Dempster–Shafer (D–S) theory of evidence. Our definition shares many of the properties of the expectation operator in probability theory. Also, for Bayesian belief functions, our definition provides the same expected value as the probabilistic expectation operator. A traditional method of computing expected of real-valued functions is to first transform a D–S belief function to a corresponding probability mass function, and then use the expectation operator for probability mass functions. Transforming a belief function to a probability function involves loss of information. Our expectation operator works directly with D–S belief functions. Another definition is using Choquet integration, which assumes belief functions are credal sets, i.e. convex sets of probability mass functions. Credal sets semantics are incompatible with Dempster's combination rule, the center-piece of the D–S theory. In general, our definition provides different expected values than, e.g. if we use probabilistic expectation using the pignistic transform or the plausibility transform of a belief function. Using our definition of expectation, we provide new definitions of variance, covariance, correlation, and other higher moments and describe their properties.

    更新日期:2020-01-21
  • IJGS WUPES 2018 Preface
    Int. J. Gen. Syst. (IF 2.259) Pub Date : 2019-12-10
    Giulianella Coletti; Václav Kratochvíl

    (2020). IJGS WUPES 2018 Preface. International Journal of General Systems: Vol. 49, Uncertainty Processing, pp. 1-2.

    更新日期:2020-01-04
  • Adversarial data poisoning attacks against the PC learning algorithm
    Int. J. Gen. Syst. (IF 2.259) Pub Date : 2019-06-17
    Emad Alsuwat; Hatim Alsuwat; Marco Valtorta; Csilla Farkas

    Data integrity is a key component of effective Bayesian network structure learning algorithms, namely PC algorithm, design and use. Given the role that integrity of data plays in these outcomes, this research demonstrates the importance of data integrity as a key component in machine learning tools in order to emphasize the need for carefully considering data integrity during tool development and utilization. To meet this purpose, we study how an adversary could generate a desired network with the PC algorithm. Given a Bayesian network B1 and a database DB1 generated by B1 and a second Bayesian network, B2, which is equal to B1, except for a minor change like a missing link, a reversed link, or an additional link, we explore and analyze what is the minimal number of changes such as additions, deletions, substitutions to DB1 that lead to a database DB2 that, when given as input to PC algorithm, results in B2.

    更新日期:2020-01-04
  • Probabilistic inconsistency correction for misclassification in statistical matching, with an example in health care
    Int. J. Gen. Syst. (IF 2.259) Pub Date : 2019-11-13
    Andrea Capotorti

    A recently proposed procedure for correcting inconsistent (i.e. incoherent) probability assessments is specifically tailored for the statistical matching problem with misclassification component. Such procedure is based on L1 distance minimization encoded in mixed integer programming (MIP) problems and it results particularly apt to deal with assessments stemming from different sources of information. The statistical matching problem is one of those cases. The statistical matching problem has been recently studied also inside a misclassification setting. To proceed with a correction in such a framework, if marginal assessments on the conditioning event are wanted to remain fixed, the only possible solutions are the closest Fréchet–Hoeffding bounds for the misclassification probabilities. On the contrary, if also the marginal probabilities are allowed to be modified, the L1-based procedure can be applied by a straightforward translation in an MIP problem. Such procedure is applied to a healthcare expenditures and health conditions data example.

    更新日期:2020-01-04
  • A note on the approximation of Shenoy's expectation operator using probabilistic transforms
    Int. J. Gen. Syst. (IF 2.259) Pub Date : 2019-11-21
    R. Jiroušek; V. Kratochvíl; J. Rauh

    Recently, a new way of computing an expected value in the Dempster–Shafer theory of evidence was introduced by Prakash P. Shenoy. Up to now, when they needed the expected value of a utility function in D-S theory, the authors usually did it indirectly: first, they found a probability measure corresponding to the considered belief function, and then computed the classical probabilistic expectation using this probability measure. To the best of our knowledge, Shenoy's operator of expectation is the first approach that takes into account all the information included in the respective belief function. Its only drawback is its exponential computational complexity. This is why, in this paper, we compare five different approaches defining probabilistic representatives of belief function from the point of view, which of them yields the best approximations of Shenoy's expected values of utility functions.

    更新日期:2020-01-04
  • Detecting correlation between extreme probability events
    Int. J. Gen. Syst. (IF 2.259) Pub Date : 2019-11-21
    G. Coletti; L. C. van der Gaag; D. Petturiti; B. Vantaggi

    As classical definitions of correlation give rise to counterintuitive statements when extreme probability events are involved, we introduce enhanced notions of positive and negative correlation in the general framework of coherent conditional probability. These notions allow to handle extreme probability events in a principled way by accommodating the different levels of strength of the zero probabilities involved (namely, zero layers). Since the detection of correlations by means of zero layers is computationally challenging, we provide a full characterization relying on only conditional probability values.

    更新日期:2020-01-04
  • Learning bipartite Bayesian networks under monotonicity restrictions
    Int. J. Gen. Syst. (IF 2.259) Pub Date : 2019-11-20
    Martin Plajner; Jiří Vomlel

    Learning parameters of a probabilistic model is a necessary step in machine learning tasks. We present a method to improve learning from small datasets by using monotonicity conditions. Monotonicity simplifies the learning and it is often required by users. We present an algorithm for Bayesian Networks parameter learning. The algorithm and monotonicity conditions are described, and it is shown that with the monotonicity conditions we can better fit underlying data. Our algorithm is tested on artificial and empiric datasets. We use different methods satisfying monotonicity conditions: the proposed gradient descent, isotonic regression EM, and non-linear optimization. We also provide results of unrestricted EM and gradient descent methods. Learned models are compared with respect to their ability to fit data in terms of log-likelihood and their fit of parameters of the generating model. Our proposed method outperforms other methods for small sets, and provides better or comparable results for larger sets.

    更新日期:2020-01-04
  • How to Fully Represent Expert Information about Imprecise Properties in a Computer System - Random Sets, Fuzzy Sets, and Beyond: An Overview.
    Int. J. Gen. Syst. (IF 2.259) Pub Date : 2014-11-12
    Hung T Nguyen,Vladik Kreinovich

    To help computers make better decisions, it is desirable to describe all our knowledge in computer-understandable terms. This is easy for knowledge described in terms on numerical values: we simply store the corresponding numbers in the computer. This is also easy for knowledge about precise (well-defined) properties which are either true or false for each object: we simply store the corresponding "true" and "false" values in the computer. The challenge is how to store information about imprecise properties. In this paper, we overview different ways to fully store the expert information about imprecise properties. We show that in the simplest case, when the only source of imprecision is disagreement between different experts, a natural way to store all the expert information is to use random sets; we also show how fuzzy sets naturally appear in such random-set representation. We then show how the random-set representation can be extended to the general ("fuzzy") case when, in addition to disagreements, experts are also unsure whether some objects satisfy certain properties or not.

    更新日期:2019-11-01
  • On the history of Ludwig von Bertalanffy's "General Systemology", and on its relationship to cybernetics - part III: convergences and divergences.
    Int. J. Gen. Syst. (IF 2.259) Pub Date : 2015-11-28
    Manfred Drack,David Pouvreau

    Bertalanffy's so-called "general system theory" (GST) and cybernetics were and are often confused: this calls for clarification. In this article, Bertalanffy's conceptions and ideas are compared with those developed in cybernetics in order to investigate the differences and convergences. Bertalanffy was concerned with first order cybernetics. Nonetheless, his perspectivist epistemology is also relevant with regard to developments in second order cybernetics, and the latter is therefore also considered to some extent. W. Ross Ashby's important role as mediator between GST and cybernetics is analysed. The respective basic epistemological approaches, scientific approaches and inherent world views are discussed. We underline the complementarity of cybernetic and "organismic" trends in systems research within the unitary hermeneutical framework of "general systemology".

    更新日期:2019-11-01
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