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Title:
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Spectral learning of general weighted automata via constrained matrix completion
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Author:
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Balle Pigem, Borja de; Mohri, Mehryar
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Other authors:
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Universitat Politècnica de Catalunya. Departament de Llenguatges i Sistemes Informàtics; Universitat Politècnica de Catalunya. LARCA - Laboratori d'Algorísmia Relacional, Complexitat i Aprenentatge |
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Abstract:
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Student Paper Awards NIPS 2012 |
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Abstract:
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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. |
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Abstract:
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Peer Reviewed |
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Abstract:
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Award-winning |
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Subject(s):
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-Àrees temàtiques de la UPC::Informàtica::Sistemes d'informació
-Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències
-Weighted automata
-Transductors |
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Rights:
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Document type:
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Article - Published version
Conference Object |
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