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

TL;DR

This paper introduces a robust multi-task and transfer learning method for Gaussian mixture models (GMMs) that leverages task similarities, handles outliers, and achieves optimal convergence rates, with proven theoretical guarantees and practical validation.

Contribution

It presents the first theoretical framework for multi-task and transfer learning on GMMs, including robust EM algorithms and alignment techniques for improved unsupervised learning.

Findings

Achieves minimax optimal convergence rates for GMM parameter estimation.

Effectively handles outliers and unknown task similarities.

Demonstrates superior performance in simulations and real data.

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 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.