Unsupervised Multi-Task and Transfer Learning on Gaussian
Mixture Models
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"))
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 Expectation-Maximization (EM) algorithm that not only can effectively utilize unknown similarity between related tasks but is also robust against a fraction of outlier tasks from arbitrary sources. The proposed procedure is shown to achieve 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. Finally, we demonstrate the effectiveness of our methods through simulations and a real data analysis. To the best of our knowledge, this is the first work studying multi-task and transfer learning on GMMs with theoretical guarantees. This package implements the algorithms proposed in Tian, Y., Weng, H., & Feng, Y. (2022) <arXiv:2209.15224>.
doParallel, foreach, caret, mclust, stats
Ye Tian [aut, cre],
Haolei Weng [aut],
Yang Feng [aut]

Place-holder package (roughly speaking an empty package)
for finding clusters in multivariate timeseries. Full
implementation pending.

A package for multivariate timeseries clustering.
Currently, this includes constrained agglomerative clustering
over observations (and extensions for change point detection),
based closely on the work of Harnish, Nelson and Runger (2009).
This package is incomplete and experimental.