Mixed membership Gaussians

Abstract

In recent years, there has been significant progress in unsupervised representation learning. Classical statistical and machine learning techniques can be used on these representations for downstream tasks and applications. Here, we consider an unsupervised downstream task, namely, topic modeling with mixed membership models. Prototypical mixed membership models like the latent Dirichlet allocation (LDA) topic model use only simple discrete observed features. However, state-of-the-art representations of images, text, and other modalities are given by continuous feature vectors. Therefore, we study mixed membership Gaussians that operate on continuous feature vectors. We prove that the parameters of this model can be learned efficiently and effectively by Pearson’s method of moments and corroborate our theoretical findings on synthetic data. Experiments on standard labeled image data sets show that mixed membership Gaussians on state-of-the-art image representations yield topics that are semantically meaningful, coherent, and cover the labels that have not been used during training well.