Robust Unsupervised Multi-task and Transfer Learning on Gaussian Mixture Models
This work addresses the problem of improving unsupervised learning performance in scenarios with multiple related tasks, such as in data analysis applications, but it is incremental as it extends existing methods to GMMs with theoretical backing.
The paper tackles multi-task and transfer learning for Gaussian mixture models by proposing a robust EM-based procedure that leverages similarities between tasks and handles outliers, achieving minimax optimal convergence rates for parameter estimation and mis-clustering errors.
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 effectively utilizes unknown similarities between related tasks and is robust against a fraction of outlier tasks from arbitrary distributions. 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. Additionally, iterative unsupervised multi-task and transfer learning methods may suffer from an initialization alignment problem, and two alignment algorithms are proposed to resolve the issue. Finally, we demonstrate the effectiveness of our methods through simulations and real data examples. To the best of our knowledge, this is the first work studying multi-task and transfer learning on GMMs with theoretical guarantees.