1 research outputs found
Global Convergence of Least Squares EM for Demixing Two Log-Concave Densities
This work studies the location estimation problem for a mixture of two
rotation invariant log-concave densities. We demonstrate that Least Squares EM,
a variant of the EM algorithm, converges to the true location parameter from a
randomly initialized point. We establish the explicit convergence rates and
sample complexity bounds, revealing their dependence on the signal-to-noise
ratio and the tail property of the log-concave distribution. Moreover, we show
that this global convergence property is robust under model mis-specification.
Our analysis generalizes previous techniques for proving the convergence
results for Gaussian mixtures. In particular, we make use of an
angle-decreasing property for establishing global convergence of Least Squares
EM beyond Gaussian settings, as distance contraction no longer holds
globally for general log-concave mixtures