Uncertain Bayesian Networks: Learning from Incomplete Data
This work addresses a specific limitation in probabilistic modeling for scenarios with incomplete data, representing an incremental advancement in the field.
The paper tackles the problem of learning parameter distributions for uncertain Bayesian networks when data is incomplete, improving upon existing methods that require complete data. It evaluates various approaches for learning posterior parameter distributions and assessing confidence bounds for queries.
When the historical data are limited, the conditional probabilities associated with the nodes of Bayesian networks are uncertain and can be empirically estimated. Second order estimation methods provide a framework for both estimating the probabilities and quantifying the uncertainty in these estimates. We refer to these cases as uncer tain or second-order Bayesian networks. When such data are complete, i.e., all variable values are observed for each instantiation, the conditional probabilities are known to be Dirichlet-distributed. This paper improves the current state-of-the-art approaches for handling uncertain Bayesian networks by enabling them to learn distributions for their parameters, i.e., conditional probabilities, with incomplete data. We extensively evaluate various methods to learn the posterior of the parameters through the desired and empirically derived strength of confidence bounds for various queries.