  The standard training method of Conditional Random Fields (CRFs) is very slow
for large-scale applications. As an alternative, piecewise training divides the
full graph into pieces, trains them independently, and combines the learned
weights at test time. In this paper, we present \emph{separate} training for
undirected models based on the novel Co-occurrence Rate Factorization (CR-F).
Separate training is a local training method. In contrast to MEMMs, separate
training is unaffected by the label bias problem. Experiments show that
separate training (i) is unaffected by the label bias problem; (ii) reduces the
training time from weeks to seconds; and (iii) obtains competitive results to
the standard and piecewise training on linear-chain CRFs.
