Global Convergence of EM Algorithm for Mixtures of Two Component Linear Regression

Jeongyeol Kwon, Constantine Caramanis

Published 2018-10-12Version 1

The Expectation-Maximization algorithm is perhaps the most broadly used algorithm for inference of latent variable problems. A theoretical understanding of its performance, however, largely remains lacking. Recent results established that EM enjoys global convergence for Gaussian Mixture Models. For Mixed Regression, however, only local convergence results have been established, and those only for the high SNR regime. We show here that EM converges for mixed linear regression with two components (it is known not to converge for three or more), and moreover that this convergence holds for random initialization.