Effective dimensions of partially observed polytrees

Abstract

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, the standard dimension might no longer be appropriate. Instead, an effective dimension should be used. Zhang & Kočka showed how to compute the effective dimensions of partially observed trees. In this paper we solve the same problem for partially observed polytrees.