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.

翻译：本文研究如何利用张量恢复对角高斯混合模型中的参数。首先从样本中估计高斯混合模型的高阶矩，这些估计值构成由模型隐藏参数生成的不完整对称张量。我们提出使用生成多项式来计算不完整对称张量的近似解，并利用所得分解结果恢复模型参数。理论证明当估计矩准确时，恢复的参数具有精度保证。通过使用高阶矩，该算法能够学习包含更多成分的高斯混合模型。针对给定的模型维度和阶数，我们给出了算法可计算的高斯混合模型成分数量的上限。