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

Shay B. Cohen, Karl Stratos, Michael Collins, Dean P. Foster, Lyle Ungar.

Year: 2014, Volume: 15, Issue: 69, Pages: 2399−2449


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.