Events

Unsupervised Multi-task and Transfer Learning on Gaussian Mixture Models

Speaker: Yang Feng

Location: 60 Fifth Avenue, Room 7th floor

Date: Wednesday, February 8, 2023

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 work, 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 similarities between related tasks but is also robust against a fraction of outlier tasks from arbitrary sources. The proposed procedure is shown to achieve the minimax optimal rate of convergence for both parameter estimation error and the excess mis-clustering error, in a wide range of regimes. Moreover, we generalize our approach to tackle the problem of transfer learning for GMMs, where similar theoretical results are derived. Finally, we implement the algorithms in a new R package mtlgmm and demonstrate the effectiveness of our methods  through simulations and real data analysis.  To the best of our knowledge, this is the first work studying multi-task and transfer learning on GMMs with theoretical guarantees.