Robust Unsupervised Multi-task and Transfer Learning on Gaussian Mixture Models
This paper addresses unsupervised multi-task and transfer learning for Gaussian mixture models (GMMs), tackling challenges including unknown inter-task parameter structural similarity, presence of outlier tasks, and initialization misalignment. We propose the first robust multi-task learning framework for GMMs with theoretical guarantees, featuring: (1) a weighted EM algorithm resilient to outlier tasks; (2) dual alignment—simultaneous alignment in both label space and parameter space—to mitigate initialization sensitivity; and (3) adaptive estimation of task similarity coupled with a transfer-generalization design. We establish minimax-optimal convergence rates for both parameter estimation error and misclustering error. Extensive experiments on synthetic and real-world datasets demonstrate substantial improvements over single-task baselines, yielding enhanced clustering stability and more accurate parameter estimation.