Spectral Experts for Estimating Mixtures of Linear Regressions

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 the mixture of linear regressions, a simple instance of discriminative latent-variable models. Our approach relies on a low-rank linear regression to recover a symmetric tensor, which can be factorized into the parameters using the tensor power method. We prove rates of convergence for our estimator and provide an empirical evaluation illustrating its strengths relative to local optimization (EM).