Title: Robust Unsupervised Multi-task Learning on Mixture Models

Abstract: Unsupervised learning has been widely used in many real-world applications. One of the simplest and most important unsupervised learning models is the Gaussian mixture model (GMM). In this talk, we study the multi-task learning problem on GMMs, which aims to leverage potentially similar GMM parameter structures among tasks to obtain improved learning performance compared to single-task learning. We propose a multi-task GMM learning procedure based on the EM algorithm that not only can effectively utilize unknown similarity between related tasks but is also robust against a fraction of outlier tasks from arbitrary sources. The proposed procedure is shown to achieve minimax optimal rate of convergence for both parameter estimation error and the excess mis-clustering error, in a wide range of regimes. We then generalize our approach to tackle the problem of multi-task learning for general mixture models, where a general and informative error bound is derived. The effectiveness of our methods will be demonstrated through simulations and real data examples.