Graphical Models: Methods for Data Analysis and Mining. (Book Reviews)

By Carey, Vincent J. | Journal of the American Statistical Association, March 2003 | Go to article overview

Graphical Models: Methods for Data Analysis and Mining. (Book Reviews)


Carey, Vincent J., Journal of the American Statistical Association


Christian BORGELT and Rudolf KRUSE. New York: Wiley, 2002. ISBN 0-470-84337-3. viii+ 358 pp. $79.95 (H).

In their prefatory overview to the volume Applications of Uncertainty Formalisms, Parsons and Hunter (1998) distinguished the three main numerical approaches to approximate reasoning under conditions of uncertainty: probability theory (e.g., Lindley 1975), evidence theory (Dempster 1968), and possibility theory (Zadeh 1978). Graphical Models: Methods for Data Analysis and Mining is a fairly thorough overview of the theory of graphical models, with a focus on the use of possibility measures to characterize uncertainty in the building and interpretation of these models.

The first chapter provides definitions of knowledge discovery in databases (KDD) and data mining, with brief reference lists and URLs for catalogs of related tools. In the second chapter, a five-page sketch of relational algebra and conditional probability is followed by 30 pages on possibility theory and the context model. This includes several simple examples, conducted with special dice, to compare the inferences achievable using probability and possibility measures. [For readers who have not encountered possibility theory, a key characterization is [PI](A U B) = max([PI](A), [PI](B)) and [PI](A ** B) = min({PI](A), [PI](B)), where A and B are any fuzzy subsets of a fuzzy universe governed by a possibility measure [PI].] This chapter is a reasonable mix of formalism and illustrative simple examples.

Chapter 3, "Decomposition," includes a fairly formal treatment of relational algebra sufficient to define the minimal decomposition of a relation. Relational algebra concepts are then connected with binary possibility measures to construct concepts of conditional possibility and conditional relational independence that are analogous to central concepts of probability theory for graphical models. Conditional probability and factorization of probability models are defined, and general possibilistic decompositions are developed. The chapter concludes with a section titled "Possibility versus Probability" that includes the following:

In other words, a marginal probability distribution states "the probability that attribute A has value a is p." This probability is aggregated over all values of all other attributes and thus refers to a one element vector (a). A marginal possibility distribution instead states "the degree of possibility of a value vector with the highest degree of possibility of all tuples in which attribute A has value a is p." That is, it refers to a value vector over all attributes of the universe of discourse, although the values of all attributes other than A are left implicit.

This is perhaps the most focused statement on the contrast between the possibilistic and probabilistic frameworks found in the book. It is followed by discussion of a number of caveats for the possibilistic approach.

Chapter 4 provides a formal treatment of graphical representation of statistical models, including the graphoid axioms, proof (deferred to an Appendix) that conditional possibilistic independence satisfies the semigraphoid axioms, graph theory, Markov properties, evidence propagation, and join-tree propagation.

Chapter 5 is a mainly technical treatment of computing projections of relations and marginalizations of distributions The EM algorithm and some accelerations are presented. Examples are reviewed, but the authors note that they "could not get hold of any real-world dataset containing 'true' imprecise attribute values, i.e., datasets with cases in which for an attribute A a set S [member of](A) with \S\ I and S [not equal to](A) was possible." In other words, the authors had access only to datasets in which imprecision coincided with total missingoess. Public datasets with censored variables are available to remedy this gap.

Chapter 6, "Naive Classifiers," describes the naive Bayes classifier (a graphical model with star-like structure) and its application to the iris dataset. …

The rest of this article is only available to active members of Questia

Sign up now for a free, 1-day trial and receive full access to:

  • Questia's entire collection
  • Automatic bibliography creation
  • More helpful research tools like notes, citations, and highlights
  • Ad-free environment

Already a member? Log in now.

Notes for this article

Add a new note
If you are trying to select text to create highlights or citations, remember that you must now click or tap on the first word, and then click or tap on the last word.
One moment ...
Default project is now your active project.
Project items

Items saved from this article

This article has been saved
Highlights (0)
Some of your highlights are legacy items.

Highlights saved before July 30, 2012 will not be displayed on their respective source pages.

You can easily re-create the highlights by opening the book page or article, selecting the text, and clicking “Highlight.”

Citations (0)
Some of your citations are legacy items.

Any citation created before July 30, 2012 will labeled as a “Cited page.” New citations will be saved as cited passages, pages or articles.

We also added the ability to view new citations from your projects or the book or article where you created them.

Notes (0)
Bookmarks (0)

You have no saved items from this article

Project items include:
  • Saved book/article
  • Highlights
  • Quotes/citations
  • Notes
  • Bookmarks
Notes
Cite this article

Cited article

Style
Citations are available only to our active members.
Sign up now to cite pages or passages in MLA, APA and Chicago citation styles.

(Einhorn, 1992, p. 25)

(Einhorn 25)

1

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

Cited article

Graphical Models: Methods for Data Analysis and Mining. (Book Reviews)
Settings

Settings

Typeface
Text size Smaller Larger Reset View mode
Search within

Search within this article

Look up

Look up a word

  • Dictionary
  • Thesaurus
Please submit a word or phrase above.
Print this page

Print this page

Why can't I print more than one page at a time?

Full screen

matching results for page

Cited passage

Style
Citations are available only to our active members.
Sign up now to cite pages or passages in MLA, APA and Chicago citation styles.

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn, 1992, p. 25).

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences."1

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

Cited passage

Welcome to the new Questia Reader

The Questia Reader has been updated to provide you with an even better online reading experience.  It is now 100% Responsive, which means you can read our books and articles on any sized device you wish.  All of your favorite tools like notes, highlights, and citations are still here, but the way you select text has been updated to be easier to use, especially on touchscreen devices.  Here's how:

1. Click or tap the first word you want to select.
2. Click or tap the last word you want to select.

OK, got it!

Thanks for trying Questia!

Please continue trying out our research tools, but please note, full functionality is available only to our active members.

Your work will be lost once you leave this Web page.

For full access in an ad-free environment, sign up now for a FREE, 1-day trial.

Already a member? Log in now.