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.

翻译：本文研究如何在对角高斯混合物模型中学习参数。 问题可以被表述为计算不完整的对称感应分解。 我们使用生成的多数值来计算不完整的对称感应分解和近似值。 然后, 使用 ARO 近似法来学习对角高斯混合物模型。 我们还进行稳定性分析。 当第一和第二顺序的时点足够准确时, 我们显示获得的高斯混合物模型参数也非常准确。 还提供了数值实验 。