Grafting-light
Jun Zhu, Ni Lao, Eric P. Xing · 2010
Feature selection is an important task in order to achieve better generalizability in high dimensional learning, and structure learning of Markov random fields (MRFs) can automatically discover the inherent structures underlying complex data. Both problems can be cast as solving an l1-norm regularized parameter estimation problem. The existing Grafting method can avoid doing inference on dense graphs in structure learning by incrementally selecting new features. However, Grafting performs a greedy step to optimize over free parameters once new features are included. This greedy strategy results in low efficiency when parameter learning is itself non-trivial, such as in MRFs, in which parameter learning depends on an expensive subroutine to calculate gradients. The complexity of calculating gradients in MRFs is typically exponential to the size of maximal cliques.