AISTATS 2016poster8 citations
Low-Rank Approximation of Weighted Tree Automata
Guillaume Rabusseau, Borja Balle, Shay Cohen
Abstract
We describe a technique to minimize weighted tree automata (WTA), a powerful formalisms that subsumes probabilistic context-free grammars (PCFGs) and latent-variable PCFGs. Our method relies on a singular value decomposition of the underlying Hankel matrix defined by the WTA. Our main theoretical result is an efficient algorithm for computing the SVD of an infinite Hankel matrix implicitly represented as a WTA. We evaluate our method on real-world data originating in newswire treebank. We show that the model achieves lower perplexity than previous methods for PCFG minimization, and also is much more stable due to the absence of local optima.
BibTeX
@InProceedings{pmlr-v51-rabusseau16,
title = {Low-Rank Approximation of Weighted Tree Automata},
author = {Rabusseau, Guillaume and Balle, Borja and Cohen, Shay},
booktitle = {Proceedings of the 19th International Conference on Artificial Intelligence and Statistics},
pages = {839--847},
year = {2016},
editor = {Gretton, Arthur and Robert, Christian C.},
volume = {51},
series = {Proceedings of Machine Learning Research},
address = {Cadiz, Spain},
month = {09--11 May},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v51/rabusseau16.pdf},
url = {https://proceedings.mlr.press/v51/rabusseau16.html},
abstract = {We describe a technique to minimize weighted tree automata (WTA), a powerful formalisms that subsumes probabilistic context-free grammars (PCFGs) and latent-variable PCFGs. Our method relies on a singular value decomposition of the underlying Hankel matrix defined by the WTA. Our main theoretical result is an efficient algorithm for computing the SVD of an infinite Hankel matrix implicitly represented as a WTA. We evaluate our method on real-world data originating in newswire treebank. We show that the model achieves lower perplexity than previous methods for PCFG minimization, and also is much more stable due to the absence of local optima.}
}