Eeective Dimensions of Partially Observable Polytrees

Model complexity is an important factor to consider when selecting among graphical models. When all variables are observed, the complexity of a model can be measured by its standard dimension, i.e. the number of independent parameters. When latent variables are present, however, standard dimension might no longer be appropriate. One should instead use eeective dimension 5]. Zhang & Ko cka 13] showed how to compute the eeective dimensions of partially observable trees. In this paper we solve this problem for partially observable polytrees.