  We propose and analyze a new vantage point for the learning of mixtures of
Gaussians: namely, the PAC-style model of learning probability distributions
introduced by Kearns et al. Here the task is to construct a hypothesis mixture
of Gaussians that is statistically indistinguishable from the actual mixture
generating the data; specifically, the KL-divergence should be at most epsilon.
  In this scenario, we give a poly(n/epsilon)-time algorithm that learns the
class of mixtures of any constant number of axis-aligned Gaussians in
n-dimensional Euclidean space. Our algorithm makes no assumptions about the
separation between the means of the Gaussians, nor does it have any dependence
on the minimum mixing weight. This is in contrast to learning results known in
the ``clustering'' model, where such assumptions are unavoidable.
  Our algorithm relies on the method of moments, and a subalgorithm developed
in previous work by the authors (FOCS 2005) for a discrete mixture-learning
problem.
