  Discriminative latent-variable models are typically learned using EM or
gradient-based optimization, which suffer from local optima. In this paper, we
develop a new computationally efficient and provably consistent estimator for a
mixture of linear regressions, a simple instance of a discriminative
latent-variable model. Our approach relies on a low-rank linear regression to
recover a symmetric tensor, which can be factorized into the parameters using a
tensor power method. We prove rates of convergence for our estimator and
provide an empirical evaluation illustrating its strengths relative to local
optimization (EM).
