We consider the problem of learning mixtures of generalized linear models
(GLM) which arise in classification and regression problems. Typical learning
approaches such as expectation maximization (EM) or variational Bayes can get
stuck in spurious local optima. In contrast, we present a tensor decomposition
method which is guaranteed to correctly recover the parameters. The key insight
is to employ certain feature transformations of the input, which depend on the
input generative model. Specifically, we employ score function tensors of the
input and compute their cross-correlation with the response variable. We
establish that the decomposition of this tensor consistently recovers the
parameters, under mild non-degeneracy conditions. We demonstrate that the
computational and sample complexity of our method is a low order polynomial of
the input and the latent dimensions.

本文提出了通过张量分解方法学习广义线性模型的混合模型参数的方法，通过对输入进行特征转换以及使用得分函数张量和响应变量的交叉相关计算可以得到正确的参数估计，且其计算和样本复杂度是输入和潜在维度的低阶多项式。