  This paper studies how to recover parameters in diagonal Gaussian mixture
models using tensors. High-order moments of the Gaussian mixture model are
estimated from samples. They form incomplete symmetric tensors generated by
hidden parameters in the model. We propose to use generating polynomials to
compute incomplete symmetric tensor approximations. The obtained decomposition
is utilized to recover parameters in the model. We prove that our recovered
parameters are accurate when the estimated moments are accurate. Using
high-order moments enables our algorithm to learn Gaussian mixtures with more
components. For a given model dimension and order, we provide an upper bound of
the number of components in the Gaussian mixture model that our algorithm can
compute.
