Spectral learning of general weighted automata via constrained matrix completion

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Document typeConference lecture
Defense date2012
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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.
Description
Student Paper Awards NIPS 2012
CitationB. Balle; Mohri, M. Spectral learning of general weighted automata via constrained matrix completion. A: Annual Conference on Neural Information Processing Systems. "Advances in Neural Information Processing Systems 26: proceedings of the 2012 conference". Lake Tahoe, Nevada: 2012, p. 2168-2176.
Award-winningAward-winning
Publisher versionhttp://books.nips.cc/papers/files/nips25/bibhtml/NIPS2012_1075.html
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