论文标题
过于稳定的订单-3张量分解，盲切解和高斯混合模型
Overcomplete order-3 tensor decomposition, blind deconvolution and Gaussian mixture models
论文作者
论文摘要
我们提出了一种基于Jennrich算法的张量分解算法，并将我们的新算法思想应用于盲卷曲和高斯混合模型。 Our first contribution is a simple and efficient algorithm to decompose certain symmetric overcomplete order-3 tensors, that is, three dimensional arrays of the form $T = \sum_{i=1}^n a_i \otimes a_i \otimes a_i$ where the $a_i$s are not linearly independent.Our algorithm comes with a detailed robustness analysis.我们的第二个贡献基于张量分解算法的基础，以扩大可以有效估计参数的高斯混合模型家族。这些想法也在更一般的盲型卷积框架中提出，该框架适用于相同但非常通用的分布的混合模型，包括所有中央对称分布，具有有限的第6刻。
We propose a new algorithm for tensor decomposition, based on Jennrich's algorithm, and apply our new algorithmic ideas to blind deconvolution and Gaussian mixture models. Our first contribution is a simple and efficient algorithm to decompose certain symmetric overcomplete order-3 tensors, that is, three dimensional arrays of the form $T = \sum_{i=1}^n a_i \otimes a_i \otimes a_i$ where the $a_i$s are not linearly independent.Our algorithm comes with a detailed robustness analysis. Our second contribution builds on top of our tensor decomposition algorithm to expand the family of Gaussian mixture models whose parameters can be estimated efficiently. These ideas are also presented in a more general framework of blind deconvolution that makes them applicable to mixture models of identical but very general distributions, including all centrally symmetric distributions with finite 6th moment.
