Mixture models are a staple in machine learning and applied statistics for
treating data taken from multiple sub-populations.  For many classes of
mixture models, parameter estimation is computationally and/or
information-theoretically hard in general.  In this talk, I'll describe a
method-of-moments estimator for the class of non-degenerate mixtures of
spherical Gaussians.  The estimator has polynomial computational and sample
complexity, and does not require a minimum separation on the component
means to succeed.  Previous estimators for this model class either required
the mixture components to be very well-separated, or had exponential sample
or computational complexity.