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# Some improvements of the spectral learning approach for probabilistic grammatical inference

*The 12th International Conference on Grammatical Inference*, PMLR 34:64-78, 2014.

#### Abstract

Spectral methods propose new and elegant solutions in probabilistic grammatical inference. We propose two ways to improve them. We show how a linear representation, or equivalently a weighted automata, output by the spectral learning algorithm can be taken as an initial point for the Baum Welch algorithm, in order to increase the likelihood of the observation data. Secondly, we show how the inference problem can naturally be expressed in the framework of Structured Low-Rank Approximation. Both ideas are tested on a benchmark extracted from the PAutomaC challenge.