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arXiv · 1206.6393

Local Loss Optimization in Operator Models: A New Insight into Spectral Learning

Borja Balle·Ariadna Quattoni·Xavier Carreras
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Abstract

This paper re-visits the spectral method for learning latent variable models defined in terms of observable operators. We give a new perspective on the method, showing that operators can be recovered by minimizing a loss defined on a finite subset of the domain. A non-convex optimization similar to the spectral method is derived. We also propose a regularized convex relaxation of this optimization. We show that in practice the availabilty of a continuous regularization parameter (in contrast with the discrete number of states in the original method) allows a better trade-off between accuracy and model complexity. We also prove that in general, a randomized strategy for choosing the local loss will succeed with high probability.

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Borja Balle, Ariadna Quattoni, Xavier Carreras. 2012-06-27. Local Loss Optimization in Operator Models: A New Insight into Spectral Learning. https://arxiv.org/abs/1206.6393

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