### Abstract

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.

Original language | English (US) |
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Title of host publication | Learning Theory - 20th Annual Conference on Learning Theory, COLT 2007, Proceedings |

Publisher | Springer Verlag |

Pages | 349-364 |

Number of pages | 16 |

ISBN (Print) | 9783540729259 |

DOIs | |

State | Published - 2007 |

Event | 20th Annual Conference on Learning Theory, COLT 2007 - San Diego, CA, United States Duration: Jun 13 2007 → Jun 15 2007 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 4539 LNAI |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 20th Annual Conference on Learning Theory, COLT 2007 |
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Country | United States |

City | San Diego, CA |

Period | 6/13/07 → 6/15/07 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Learning Theory - 20th Annual Conference on Learning Theory, COLT 2007, Proceedings*(pp. 349-364). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4539 LNAI). Springer Verlag. https://doi.org/10.1007/978-3-540-72927-3_26