Learning Bayesian network parameters under order constraints

We consider the problem of learning the parameters of a Bayesian network from data, while taking into account prior knowledge about the signs of influences between variables. Such prior knowledge can be readily obtained from domain experts. We show that this problem of parameter learning is a special case of isotonic regression and provide a simple algorithm for computing isotonic estimates. Our experimental results for a small Bayesian network in the medical domain show that taking prior knowledge about the signs of influences into account leads to an improved fit of the true distribution, especially when only a small sample of data is available. More importantly, however, the isotonic estimator provides parameter estimates that are consistent with the specified prior knowledge, thereby resulting in a network that is more likely to be accepted by experts in its domain of application.