Semirings, automata, languages
Semirings, automata, languages
A training algorithm for optimal margin classifiers
COLT '92 Proceedings of the fifth annual workshop on Computational learning theory
Machine Learning
Generalization performance of support vector machines and other pattern classifiers
Advances in kernel methods
Automata, Languages, and Machines
Automata, Languages, and Machines
Automata: Theoretic Aspects of Formal Power Series
Automata: Theoretic Aspects of Formal Power Series
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
Finite-state transducers in language and speech processing
Computational Linguistics
Rational Kernels: Theory and Algorithms
The Journal of Machine Learning Research
Moment Kernels for Regular Distributions
Machine Learning
Introduction to probabilistic automata (Computer science and applied mathematics)
Introduction to probabilistic automata (Computer science and applied mathematics)
Kernel methods for learning languages
Theoretical Computer Science
Learning linearly separable languages
ALT'06 Proceedings of the 17th international conference on Algorithmic Learning Theory
Learning rational stochastic languages
COLT'06 Proceedings of the 19th annual conference on Learning Theory
Efficient computation of the relative entropy of probabilistic automata
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
Kernel methods for learning languages
Theoretical Computer Science
String Kernels Based on Variable-Length-Don't-Care Patterns
DS '08 Proceedings of the 11th International Conference on Discovery Science
On the learnability of shuffle ideals
ALT'12 Proceedings of the 23rd international conference on Algorithmic Learning Theory
Rational kernels for arabic text classification
SLSP'13 Proceedings of the First international conference on Statistical Language and Speech Processing
On the learnability of shuffle ideals
The Journal of Machine Learning Research
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We present a general study of learning and linear separability with rational kernels, the sequence kernels commonly used in computational biology and natural language processing. We give a characterization of the class of all languages linearly separable with rational kernels and prove several properties of the class of languages linearly separable with a fixed rational kernel. In particular, we show that for kernels with transducer values in a finite set, these languages are necessarily finite Boolean combinations of preimages by a transducer of a single sequence. We also analyze the margin properties of linear separation with rational kernels and show that kernels with transducer values in a finite set guarantee a positive margin and lead to better learning guarantees. Creating a rational kernel with values in a finite set is often non-trivial even for relatively simple cases. However, we present a novel and general algorithm, double-tape disambiguation, that takes as input a transducer mapping sequences to sequence features, and yields an associated transducer that defines a finite range rational kernel. We describe the algorithm in detail and show its application to several cases of interest.