By Christian Borgelt, Matthias Steinbrecher, Professor Dr Rudolf R Kruse
Graphical versions are of accelerating significance in utilized facts, and specifically in information mining. offering a self-contained creation and evaluation to studying relational, probabilistic, and possibilistic networks from facts, this moment version of Graphical versions is carefully up-to-date to incorporate the most recent learn during this burgeoning box, together with a brand new bankruptcy on visualization. The textual content offers graduate scholars, and researchers with all of the worthy history fabric, together with modelling less than uncertainty, decomposition of distributions, graphical illustration of distributions, and functions on the subject of graphical types and difficulties for extra study.
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Extra info for Graphical Models: Representations for Learning, Reasoning and Data Mining, Second Edition (Wiley Series in Computational Statistics)
Sample text
Thus our intuition, exemplified by how the word ‘‘possible’’ is used in colloquial language, does not help us much if we want to understand what may be meant by a degree of possibility. Unfortunately, this fact is often treated too lightly in publications on possibility theory. It is rarely easy to pin down the exact meaning that is given to a degree of possibility. To avoid such problems, we explain in detail a specific interpretation that is based on the context model [Gebhardt and Kruse 22 CHAPTER 2.
38 CHAPTER 2. 14 Degrees of possibility of an inconsistent random set. numbers 1–4 5–6 7–8 9–10 11–12 degree of possibility 1 5 + 1 5 1 5 + + 1 5 1 5 1 5 + + + 1 5 1 5 1 5 1 5 = = = + 1 5 1 5 = = 4 5 3 5 2 5 2 5 1 5 To make this more precise, let us consider yet another version of the dice experiment. Suppose that we have the usual five shakers with an unknown number of tetrahedrons in the first, hexahedrons in the second, and so on, but with the dodecahedrons in the fifth shaker replaced by tetrahedrons.
Therefore let us consider an experiment in which we do not have full information. Suppose that we still have five shakers, one of which is selected by rolling an icosahedron. Let us assume that we know about the kind of the dice that are contained in each shaker, that is, tetrahedrons in shaker 1, hexahedrons in shaker 2 and so on. However, let it be unknown how many dice there are in each shaker and what the rule is, by which the final outcome is determined, that is, whether the maximum number counts, or the minimum, or whether the outcome is computed as an average rounded to the nearest integer number, or whether it is determined in some other, more complicated way.