Kernel methods for learning languages

This paper studies a novel paradigm for learning formal languages from positive and negative examples which consists of mapping strings to an appropriate highdimensional feature space and learning a separating hyperplane in that space. Such mappings can often be represented flexibly with string kernels, with the additional benefit of computational efficiency. The paradigm inspected can thus be viewed as that of using kernel methods for learning languages. We initiate the study of the linear separability of automata and languages by examining the rich class of piecewise-testable languages. We introduce a subsequence feature mapping to a Hilbert space and prove that piecewise-testable languages are linearly separable in that space. The proof makes use of word combinatorial results relating to subsequences. We also show that the positive definite symmetric kernel associated to this embedding is a rational kernel and show that it can be computed in quadratic time using general-purpose wei...

• Type: Journal
• Year: 2008
• Where: TCS
• Authors: Leonid Kontorovich, Corinna Cortes, Mehryar Mohri
• Keywords: Linear Separability, Piecewise-testable Languages, Separating Hyperplane, TCS 2008, Theoretical Computer Science