Data Mining with Graphical Models

Question

1. What contributions have the authors mentioned in the paper "Data mining with graphical models" ?

2. What are the future works in "Data mining with graphical models" ?

3. What is the axiomatic framework of a valuation-based system?

4. Why are large databases maintained in almost every company?

Accepted Answer

In this paper the authors study a popular technique from its arsenal of methods to do dependency analysis, namely learning inference networks ( also called “ graphical models ” ) from data.. The authors review the already well-known probabilistic networks and provide an introduction to the recently developed and closely related possibilistic networks.

Accepted Answer

In this paper the authors reviewed, although briefly, the ideas underlying probabilistic networks and provided an equally brief introduction to possibilistic networks.. Whereas in order to learn a probabilistic network these tuples have to be discarded or treated in some complicated manner, possibilistic network learning can easily take them into account and can thus, without problem, make use of all available information.

Accepted Answer

The axiomatic framework of a valuationbased system [32] can represent various uncertainty calculi such as probability theory, Dempster-Shafer theory, and possibility theory.

Accepted Answer

Due to the advances in hardware and software technology, large databases (product databases, customer databases, etc.) are nowadays maintained in almost every company and scientific or administrational institution.

Accepted Answer

The most popular kind of probabilistic graphical models in artificial intelligence is the Bayesian network, also called belief network [26].

Accepted Answer

Since the pairwise Markov property refers to the independence of only two attributes, it would be most natural (at least for undirected graphs) to use it to define an independence graph:

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A popular method for this task is the automatic induction of inference networks, also called graphical models [36, 20], from a set of sample cases.

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Unfortunately probabilistic graphical models suffer from severe difficulties to deal with imprecise, i.e. set-valued, information in the database to learn from.

Accepted Answer

It should be emphasized, that, as already discussed above, an essential advantage of possibilistic networks over probabilistic ones is their ability to deal with imprecision, i.e. multi-valued, information.

Accepted Answer

The reasoning process, which the authors describe here exemplary for an undirected graph, basically is this: Information obtained e.g. by observations about the values of an attribute is extended to the distributions on all hyperedges containing the attribute and then projected to the intersections of these hyperedges with other hyperedges.

Accepted Answer

Its drawback, which consists in the fact that it needs a topological order of the attributes, can be overcome by a hybrid algorithm [33], which combines CI tests (to find a topological order) and K2 (to construct the Bayesian network with respect to this topological order).

Accepted Answer

P ({c}) is the (subjective) probability of the (occurrence or selection of the) context c.A set γ(c) is assumed to be the most specific correct set-valued specification of ω0, which is implied by the frame conditions that characterize the context c.

Accepted Answer

It is obvious that storing the generic knowledge directly, i.e. the distribution D, would make reasoning very simple, since then the authors only have to select all ω ∈

Accepted Answer

With these presuppositions the reasoning space in which all inferences take place is the joint domain Ω = dom(A(1)) × · · · × dom(A(m)), which is sometimes called the universe of discourse.

Data Mining with Graphical Models

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Most frequently asked questions

1. What contributions have the authors mentioned in the paper "Data mining with graphical models" ?

2. What are the future works in "Data mining with graphical models" ?

3. What is the axiomatic framework of a valuation-based system?

4. Why are large databases maintained in almost every company?

5. What is the popular kind of probabilistic graphical models in artificial intelligence?

6. What is the natural way to define an independence graph?

7. What is the popular method for inference networks?

8. What are the main problems of probabilistic graphical models?

9. What is the advantage of possibilistic networks over probabilistic ones?

10. What is the reasoning process for a graph?

11. What is the drawback of the Bayesian network?

12. What is the probability of the occurrence or selection of the context c?

13. What is the way to store the generic knowledge?

14. What is the reasoning space in which all inferences take place?

Figures

Citations

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References

Maximum likelihood from incomplete data via the EM algorithm

Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference

A mathematical theory of evidence

The concept of a linguistic variable and its application to approximate reasoning—II☆

Fuzzy sets as a basis for a theory of possibility

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