Unsupervised estimation of latent variable models is a fundamental problem
central to numerous applications of machine learning and statistics. This work
presents a principled approach for estimating broad classes of such models,
including probabilistic topic models and latent linear Bayesian networks, using
only second-order observed moments. The sufficient conditions for
identifiability of these models are primarily based on weak expansion
constraints on the topic-word matrix, for topic models, and on the directed
acyclic graph, for Bayesian networks. Because no assumptions are made on the
distribution among the latent variables, the approach can handle arbitrary
correlations among the topics or latent factors. In addition, a tractable
learning method via $\ell_1$ optimization is proposed and studied in numerical
experiments.

本文提出了一个基于二阶可观测矩的无监督估计潜变量模型的方法，包括概率主题模型和潜线性贝叶斯网络等广泛的模型，且不需要对潜变量的分布做出任何假设，可以处理主题或潜因子之间的任意相关性，并且提出了一个可行的学习方法通过 L1 优化在数值实验中进行了研究。