Dear Julie:
On Thu, 6 Apr 2000, Zhu wrote:
> Hello all,
>
> Is there any algorithms of Bayesian Network to work directly on the
> mixture of continuous and categorical variables?
>
> The classification problem that I am working on has 37 input variables, 15
> of them are categorical and the rest of them are continuous. To my
> understanding, I need to discretize the continuous varibles in order to
> apply some commonly used algorithms (such as junction tree) to construct
> and estimate BNs. Since a large portion of the input variables are
> continuous, I am afraid of loss of information by discretizing them.
> References and input on working directly on the mixture will
> be highly appreciated. I would also like to have any comments and
> experiences on how much gain we can get from working on the mixture
> directly over transforming all variables into discrete. Thanks.
I suspect that you have already discovered the work by Lauritzen on mixed
models, which is implemented in Hugin. (See, e.g., Kristian
G. Olesen. "Causal Probabilistic Networks with Both Discrete and
Continuous Variables." _IEEE Transactions on PAMI_, 15, 3 (Match 1993),
275-279.) There is some related ongoing work at Aalborg university, so
you may want to contact Kristian directly: kgo@cs.auc.dk. (Sorry,
Kristian! :-)
While this is not a direct answer to your question, I would like to report
on the experience of my former student, Leszek Piatkiewicz. In his MS
Thesis, "On the Construction of a Bayesian Network for Agricultural Loan
Assessment," he describes a classification system for loans to Canadian
farmers in Saskatchewan. The system was built from a dataset of 1999
(yes, almost two thousand) loans. Each loan was described by seven
variables, six of which are continuous (in addition to a binary class
variables). The data set did not contain any two cases with all input
variables the same but different values of the class variables.
Therefore, the optimal Bayesian classifier gave 100% accuracy. Leszek
discretized the variables using a few different techniques and found that
a small number of intervals (about 10) was sufficient to achieve 100%
classification accuracy. He inferred that discretization was a viable
option for a Bayesian network classifier, and went on to apply a variety
of learning algorithms with a variety of discretization methods.
Again, this does not answer your question, but you may also like to run
some simple experiments with discretization methods on sets of cases.
>
> Best regards,
>
> Julie
>
>
Best regards and good luck in your work!
Marco
Marco Valtorta, Associate Professor (on sabbatical leave in 1999/2000)
Department of Computer Science mgv@usceast.cs.sc.edu, mgv@cs.auc.dk (March)
University of South Carolina tel.: (1)(803)777-4641 fax: -3767
Columbia, SC 29208, U.S.A. http://www.cs.sc.edu/~mgv/ tlx: 805038 USC
- ---------------------------------------------------------------------------
"Probability is not about numbers. It is about the structure of reasoning."
--Glenn Shafer
- ---------------------------------------------------------------------------
------- End of Forwarded Message
This archive was generated by hypermail 2b29 : Fri Apr 07 2000 - 11:31:37 PDT