Dynamic labeling and tree kernels with gap penalties

Positive definiteness and computational efficiency are two important factors in designing kernels. In this paper, we focus on kernels for trees, and show an important and useful technique to design positive definite tree kernels that can be computed efficiently based on the dynamic programming methodology. We call the technique dynamic labeling. In combination with the partitionable string kernel technique, this technique yields a useful framework to design tree kernels that has a much wider range of application compared with the framework known in the literature.