In this paper, we propose a new framework for constructing text metrics which can be used to compare and support inferences among terms and sets of terms. Our metric is derived from data-driven kernels on graphs that let us capture global relations among terms and sets of terms, regardless of their complexity and size. To compute the metric efficiently for any two subsets of terms, we develop an approximation technique that relies on the precompiled term-term similarities. To scale-up the approach to problems with huge number of terms, we develop and experiment with a solution that subsamples the term space. We demonstrate the benefits of the whole framework on two text inference tasks: prediction of terms in the article from its abstract and query expansion in information retrieval.