{ "_id": "6a1bfff61d7bb097a0a291ad", "Package": "mtlgmm", "Type": "Package", "Title": "Unsupervised Multi-Task and Transfer Learning on Gaussian\nMixture Models", "Version": "0.1.0", "Authors@R": "c(person(\"Ye\", \"Tian\", role = c(\"aut\", \"cre\"), email = \"ye.t@columbia.edu\"), person(\"Haolei\", \"Weng\", role = \"aut\", email = \"wenghaol@msu.edu\"), person(\"Yang\", \"Feng\", role = \"aut\", email = \"yang.feng@nyu.edu\"))", "Description": "Unsupervised learning has been widely used in many\nreal-world applications. One of the simplest and most important\nunsupervised learning models is the Gaussian mixture model\n(GMM). In this work, we study the multi-task learning problem\non GMMs, which aims to leverage potentially similar GMM\nparameter structures among tasks to obtain improved learning\nperformance compared to single-task learning. We propose a\nmulti-task GMM learning procedure based on the\nExpectation-Maximization (EM) algorithm that not only can\neffectively utilize unknown similarity between related tasks\nbut is also robust against a fraction of outlier tasks from\narbitrary sources. The proposed procedure is shown to achieve\nminimax optimal rate of convergence for both parameter\nestimation error and the excess mis-clustering error, in a wide\nrange of regimes. Moreover, we generalize our approach to\ntackle the problem of transfer learning for GMMs, where similar\ntheoretical results are derived. Finally, we demonstrate the\neffectiveness of our methods through simulations and a real\ndata analysis. To the best of our knowledge, this is the first\nwork studying multi-task and transfer learning on GMMs with\ntheoretical guarantees. This package implements the algorithms\nproposed in Tian, Y., Weng, H., & Feng, Y. 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