Comparison of local and global undirected graphical models

CRFs are discriminative undirected models which are globally normalized. Global normalization preserves CRFs from the label bias problem which most local models suffer from. Recently proposed co-occurrence rate networks (CRNs) are also discriminative undirected models. In contrast to CRFs, CRNs are locally normalized. It was established that CRNs are immune to the label bias problem even they are local models. In this paper, we further compare ECRNs (using fully empirical relative frequencies, not by support vector regression) and CRFs. The connection between Co-occurrence Rate, which is the exponential function of pointwise mutual information, and Copulas is built in continuous case. Also they are further evaluated statistically by experiments.