Learning Bayesian network parameters under equivalence constraints

We propose a principled approach for learning parameters in Bayesian networks from incomplete datasets, where the examples of a dataset are subject to equivalence constraints. These equivalence constraints arise from datasets where examples are tied together, in that we may not know the value of a particular variable, but whatever that value is, we know it must be the same across different examples. We formalize the problem by defining the notion of a constrained dataset and a corresponding constrained likelihood that we seek to optimize. We further propose a new learning algorithm that can effectively learn more accurate Bayesian networks using equivalence constraints, which we demonstrate empirically. Moreover, we highlight how our general approach can be brought to bear on more specialized learning tasks, such as those in semi-supervised clustering and topic modeling, where more domain-specific approaches were previously developed.