Predicting {0,1}-functions on randomly drawn points
COLT '88 Proceedings of the first annual workshop on Computational learning theory
Handbook of theoretical computer science (vol. B)
A training algorithm for optimal margin classifiers
COLT '92 Proceedings of the fifth annual workshop on Computational learning theory
The minimum consistent DFA problem cannot be approximated within any polynomial
Journal of the ACM (JACM)
Efficient learning of typical finite automata from random walks
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
An introduction to computational learning theory
An introduction to computational learning theory
Machine Learning
Formal languages: an introduction and a synopsis
Handbook of formal languages, vol. 1
On the learnability and usage of acyclic probabilistic finite automata
Journal of Computer and System Sciences - Special issue on the eighth annual workshop on computational learning theory, July 5–8, 1995
Generalization performance of support vector machines and other pattern classifiers
Advances in kernel methods
Inference of Reversible Languages
Journal of the ACM (JACM)
Learning Subsequential Transducers for Pattern Recognition Interpretation Tasks
IEEE Transactions on Pattern Analysis and Machine Intelligence
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
Rational Kernels: Theory and Algorithms
The Journal of Machine Learning Research
Applied Combinatorics on Words (Encyclopedia of Mathematics and its Applications)
Applied Combinatorics on Words (Encyclopedia of Mathematics and its Applications)
Learning languages with rational kernels
COLT'07 Proceedings of the 20th annual conference on Learning theory
Learning linearly separable languages
ALT'06 Proceedings of the 17th international conference on Algorithmic Learning Theory
Learning languages with rational kernels
COLT'07 Proceedings of the 20th annual conference on Learning theory
Estimating strictly piecewise distributions
ACL '10 Proceedings of the 48th Annual Meeting of the Association for Computational Linguistics
ACL '10 Proceedings of the 48th Annual Meeting of the Association for Computational Linguistics
On languages piecewise testable in the strict sense
MOL'07/09 Proceedings of the 10th and 11th Biennial conference on The mathematics of language
Factor and subsequence kernels and signatures of rational languages
CIAA'12 Proceedings of the 17th international conference on Implementation and Application of Automata
On the learnability of shuffle ideals
ALT'12 Proceedings of the 23rd international conference on Algorithmic Learning Theory
On the learnability of shuffle ideals
The Journal of Machine Learning Research
| Hi-index | 5.23 |
This paper studies a novel paradigm for learning formal languages from positive and negative examples which consists of mapping strings to an appropriate high-dimensional 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 weighted automata algorithms. Our examination of the linear separability of piecewise-testable languages leads us to study the general problem of separability with other finite regular covers. We show that all languages linearly separable under a regular finite cover embedding, a generalization of the subsequence embedding we use, are regular. We give a general analysis of the use of support vector machines in combination with kernels to determine a separating hyperplane for languages and study the corresponding learning guarantees. Our analysis includes several additional linear separability results in abstract settings and partial characterizations for the linear separability of the family of all regular languages.