Belief Functions Based Parameter and Structure Learning of Bayesian Networks in the Presence of Missing Data^*

Article type: Research Article

Authors: Haider, Sajjad

Affiliations: George Mason University, System Architectures Laboratory, Fairfax, VA, USA. [email protected]

Note: [*] This research was sponsored in part by the Office of Naval Research under grant no. N00014-03-1-0033.

Abstract: Existing methods of parameter and structure learning of Bayesian Networks (BNs) from a database assume that the database is complete. If there are missing values, they are assumed to be missing at random. This paper incorporates the concepts used in Dempster-Shafer theory of belief functions to learn both the parameters and structure of BNs. Instead of filling the missing values by their estimates, as it is done in the conventional techniques, the proposed approach models the missing values as representing ignorance or lack of belief of a system modeler in the actual state of the corresponding variables. The proposed representation modifies the existing algorithms for parameter and structure learning of BNs. The representation also allows a system modeler to add new findings in terms of support functions as used in belief functions theory; thus, providing a richer way to enter evidence in BNs.

Keywords: Bayesian Networks, Bayesian Learning, Belief Functions, Dempster-Shafer Theory

DOI: 10.3233/HIS-2004-13-405

Journal: International Journal of Hybrid Intelligent Systems, vol. 1, no. 3-4, pp. 164-175, 2004