## Spectral Learning of Latent-Variable PCFGs: Algorithms and Sample Complexity

Shay B. Cohen, Karl Stratos, Michael Collins, Dean P. Foster, Lyle Ungar; 15(Jul):2399−2449, 2014.

### Abstract

We introduce a spectral learning algorithm for latent-variable PCFGs (Matsuzaki et al., 2005; Petrov et al., 2006). Under a separability (singular value) condition, we prove that the method provides statistically consistent parameter estimates. Our result rests on three theorems: the first gives a tensor form of the inside- outside algorithm for PCFGs; the second shows that the required tensors can be estimated directly from training examples where hidden-variable values are missing; the third gives a PAC-style convergence bound for the estimation method.

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