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Computing the Decomposable Entropy of Graphical Belief Function Models
Jiroušek, Radim ; Kratochvíl, Václav ; Shenoy, P. P.
In 2018, Jiroušek and Shenoy proposed a definition of entropy for Dempster-Shafer (D-S) belief functions called decomposable entropy. Here, we provide an algorithm for computing the decomposable entropy of directed graphical D-S belief function models. For undirected graphical belief function models, assuming that each belief function in the model is non-informative to the others, no algorithm is necessary. We compute the entropy of each belief function and add them together to get the decomposable entropy of the model. Finally, the decomposable entropy generalizes Shannon’s entropy not only for the probability of a single random variable but also for multinomial distributions expressed as directed acyclic graphical models called Bayesian networks.
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A Step towards Upper-bound of Conflict of Belief Functions based on Non-conflicting Parts
Daniel, M. ; Kratochvíl, Václav
This study compares the size of conflict based on non-conflicting parts of belief functions $Conf$ with the sum of all multiples of bbms of disjoint focal elements of belief functions in question. In general, we make an effort to reach a simple upper bound function for $Conf$. (Nevertheless, the maximal value of conflict is, of course, equal to 1 for fully conflicting belief functions). We apply both theoretical research using the recent results on belief functions and also experimental computational approach here.
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Bayesian Networks for the Analysis of Subjective Well-Being
Švorc, Jan ; Vomlel, Jiří
We use Bayesian Networks to model the influence of diverse socio-economic factors on subjective well-being and their interrelations. The classical statistical analysis aims at finding significant explanatory variables, while Bayesian Networks can also help sociologists to explain and visualize the problem in its complexity. Using Bayesian Networks the sociologists may get a deeper insight into the interplay of all measured factors and their influence on the variable of a special interest. In the paper we present several Bayesian Network models -- each being optimal from a different perspective. We show how important it is to pay a special attention to a local structure of conditional probability tables. Finally, we present results of an experimental evaluation of the suggested approaches based on real data from a large international survey. We believe that the suggested approach is well applicable to other sociological problems and that Bayesian Networks represent a new valuable tool for sociological research.
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