Robust Unsupervised Multi-Task and Transfer Learning on Gaussian Mixture Models

• 成果类型: Article; Early Access
• 署名作者: Tian, Ye; Weng, Haolei; Xia, Lucy; Feng, Yang
• 署名单位: Columbia University; Michigan State University; Hong Kong University of Science & Technology; New York University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459; 1537-274X
• DOI: 10.1080/01621459.2026.2670031
• 发表日期: 2026-06-26
• 关键词: em algorithm; Gaussian mixture models; Minimax Rate; multi-task learning; Robustness; Transfer Learning; unsupervised learning; maximum-likelihood; em algorithm; CLASSIFICATION; CONVERGENCE; EFFICIENCY

摘要

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 uses 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 the 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. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.