  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.
