Bound and Collapse

Origins: The origins of BC are in a robust method [4,5] able to learn conditional probabilities from incomplete databases based on probability intervals. This robust method computes the extreme probability distributions consistent with the available information in the database.

Method: BC is defined by two steps: i) Bound the set of estimates consistent with the available information using the robust method mentioned above, and ii) Collapse the resulting set to a point estimate via a convex combination of the extreme points, with weights depending on the assumed pattern of missing data.

Applications: BC is a general method to learn conditional probabilities from incomplete databases. So far, it has been implemented in Bayesian Knowledge Discoverer and it has been used to:

Parameter estimation: Learn the conditional probabilities rom incomplete databases.
Model Selection: Extract the graphical model defining a BBN from incomplete databases.

1. M. Ramoni and P. Sebastiani, Efficient Parameter Learning in Bayesian Networks from Incomplete Databases, Technical Report KMi-TR-41, Knowledge Media Institute, The Open University, January 1997.
2. M. Ramoni and P. Sebastiani, Learning Bayesian Networks from Incomplete Databases, Technical Report KMi-TR-43, Knowledge Media Institute, The Open University, February 1997. Also in Proceedings of the Thirteenth Conference on Uncertainty in Artificial Intelligence, Morgan Kaufman, San Mateo (CA), 1997.
3. M. Ramoni and P. Sebastiani, The Use of Exogenous Knowledge to Learn Bayesian Networks from Incomplete Databases, Technical Report KMi-TR-44, Knowledge Media Institute, The Open University, February 1997. Also in in Proceedings of the Second International Symposium on Intelligent Data Analysis, Springer Verlag, New York (NY), 1997, to appear.
4. M. Ramoni and P. Sebastiani, Discovering Bayesian Networks in Incomplete Databases, Technical Report KMi-TR-46, Knowledge Media Institute, The Open University, March 1997.