论文标题
通过隐张张量分解的非参数混合模型的力矩估计
Moment Estimation for Nonparametric Mixture Models Through Implicit Tensor Decomposition
论文作者
论文摘要
我们提出了一种交替的最小二乘类型数值优化方案，以在$ \ mathbb {r}^n $中估算有条件独立的混合模型，而无需参数化分布。遵循时刻的方法，我们解决了一个不完整的张量分解问题，以学习混合权重和分类的手段。然后，我们通过线性溶液计算组件分布的累积分布函数，较高的力矩和其他统计数据。对于高维度的计算至关重要的是，通过开发有效的无张量操作来避免与高阶张量相关的陡峭成本。数值实验证明了该算法的竞争性能及其对许多模型和应用的适用性。此外，我们提供理论分析，从混合物的低阶矩中确定可识别性，并保证ALS算法的局部线性收敛。
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.
