Effective dimensions of partially observed polytrees

Model complexity is an important factor to consider when selecting among Bayesian network models. When all variables are observed, the complexity of a model can be measured by its standard dimension, i.e., the number of linearly independent network parameters. When latent variables are present, however, standard dimension is no longer appropriate and effective dimension should be used instead [Proc. 12th Conf. Uncertainty Artificial Intell. (1996) 283]. Effective dimensions of Bayesian networks are difficult to compute in general. Work has begun to develop efficient methods for calculating the effective dimensions of special networks. One such method has been developed for partially observed trees [J. Artificial Intell. Res. 21 (2004) 1]. In this paper, we develop a similar method for partially observed polytrees.