Learning Belief Networks in the Presence of Missing Values
and Hidden Variables
To appear in Fourteenth
Inter. Conf. on Machine Learning (ICML97).
In recent years there has been a flurry of works on learning
probabilistic belief networks. Current state of the art
methods have been shown to be successful for two learning scenarios:
learning both network structure and parameters from complete
data, and learning parameters for a fixed network from
incomplete data---that is, in the presence of missing values
---or hidden variables. However, no method has yet been demonstrated to
effectively learn network structure from incomplete data.
In this paper, we propose a new method for learning network structure
from incomplete data. This method is based on an extension of the
Expectation-Maximization (EM) algorithm for model selection
problems that performs search for the best structure inside
the EM procedure. We prove the convergence of this algorithm, and adapt
it for learning belief networks. We then describe how to learn
networks in two scenarios: when the data contains missing values, and
in the presence of hidden variables. We provide experimental results
that show the effectiveness of our procedure in both scenarios.
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