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For an application problem, there may be multiple databases, and each database may not contain complete variables or attributes, that is, some variables are observed but some others are missing. Further, data of a database may be collected conditionally on some designed variables. In this paper, we discuss problems related to data mining from such multiple databases. We propose an approach for detecting identifiability of a joint distribution from multiple databases. For an identifiable joint distribution, we further present the expectation-maximization (EM) algorithm for calculating the maximum likelihood estimates (MLEs) of the joint distribution.

Identifiability and Estimation of Probabilities from Multiple Databases with Incomplete Data and Sampling Selection