We present an alternating least squares type numerical optimization scheme to estimate conditionally-independent mixture models in $\mathbb{R}^n$, without parameterizing the distributions. Following the method of moments, we tackle an incomplete tensor decomposition problem to learn the mixing weights and componentwise means. Then we compute the cumulative distribution functions, higher moments and other statistics of the component distributions through linear solves. Crucially for computations in high dimensions, the steep costs associated with high-order tensors are evaded, via the development of efficient tensor-free operations. Numerical experiments demonstrate the competitive performance of the algorithm, and its applicability to many models and applications. Furthermore we provide theoretical analyses, establishing identifiability from low-order moments of the mixture and guaranteeing local linear convergence of the ALS algorithm.

翻译：我们提出了一种交替最小二乘类型的数值优化方案，用于估计$\mathbb{R}^n$中条件独立的混合模型，无需对分布进行参数化。遵循矩方法，我们解决了一个不完整张量分解问题，以学习混合权重和分量均值。然后通过线性求解计算累积分布函数、高阶矩以及分量分布的其他统计量。关键是在高维计算中，通过开发高效的免张量操作，规避了高阶张量带来的高昂成本。数值实验展示了该算法的竞争性能及其对多种模型和应用的适用性。此外，我们提供了理论分析，建立了基于混合低阶矩的可识别性，并保证了ALS算法的局部线性收敛性。