  This paper studies how to learn parameters in diagonal Gaussian mixture
models. The problem can be formulated as computing incomplete symmetric tensor
decompositions. We use generating polynomials to compute incomplete symmetric
tensor decompositions and approximations. Then the tensor approximation method
is used to learn diagonal Gaussian mixture models. We also do the stability
analysis. When the first and third order moments are sufficiently accurate, we
show that the obtained parameters for the Gaussian mixture models are also
highly accurate. Numerical experiments are also provided.
