Spectral learning of general weighted automata via constrained matrix completion

Borja Balle, Mehryar Mohri

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Many tasks in text and speech processing and computational biology require estimating functions mapping strings to real numbers. A broad class of such functions can be defined by weighted automata. Spectral methods based on the singular value decomposition of a Hankel matrix have been recently proposed for learning a probability distribution represented by a weighted automaton from a training sample drawn according to this same target distribution. In this paper, we show how spectral methods can be extended to the problem of learning a general weighted automaton from a sample generated by an arbitrary distribution. The main obstruction to this approach is that, in general, some entries of the Hankel matrix may be missing. We present a solution to this problem based on solving a constrained matrix completion problem. Combining these two ingredients, matrix completion and spectral method, a whole new family of algorithms for learning general weighted automata is obtained. We present generalization bounds for a particular algorithm in this family. The proofs rely on a joint stability analysis of matrix completion and spectral learning.

Original languageEnglish (US)
Title of host publicationAdvances in Neural Information Processing Systems 25
Subtitle of host publication26th Annual Conference on Neural Information Processing Systems 2012, NIPS 2012
Pages2159-2167
Number of pages9
StatePublished - 2012
Event26th Annual Conference on Neural Information Processing Systems 2012, NIPS 2012 - Lake Tahoe, NV, United States
Duration: Dec 3 2012Dec 6 2012

Publication series

NameAdvances in Neural Information Processing Systems
Volume3
ISSN (Print)1049-5258

Other

Other26th Annual Conference on Neural Information Processing Systems 2012, NIPS 2012
CountryUnited States
CityLake Tahoe, NV
Period12/3/1212/6/12

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing

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