A new parameter Learning Method for Bayesian Networks with Qualitative Influences
This work addresses parameter estimation for Bayesian networks with ordered variables, offering a more efficient computational method, but it is incremental as it builds directly on prior research.
The authors tackled parameter learning in Bayesian networks with qualitative influences by extending a previous method from binary to ordered discrete variables, proposing an isotonic regression-based estimator that is computationally simpler than constrained maximum likelihood estimation. Experiments on simulated and real data showed the new method is competitive with the constrained estimator and both outperform the standard estimator.
We propose a new method for parameter learning in Bayesian networks with qualitative influences. This method extends our previous work from networks of binary variables to networks of discrete variables with ordered values. The specified qualitative influences correspond to certain order restrictions on the parameters in the network. These parameters may therefore be estimated using constrained maximum likelihood estimation. We propose an alternative method, based on the isotonic regression. The constrained maximum likelihood estimates are fairly complicated to compute, whereas computation of the isotonic regression estimates only requires the repeated application of the Pool Adjacent Violators algorithm for linear orders. Therefore, the isotonic regression estimator is to be preferred from the viewpoint of computational complexity. Through experiments on simulated and real data, we show that the new learning method is competitive in performance to the constrained maximum likelihood estimator, and that both estimators improve on the standard estimator.