The article considers semi-supervised multitask learning on a Gaussian mixture model (GMM). Using methods from statistical physics, we compute the asymptotic Bayes risk of each task in the regime of large datasets in high dimension, from which we analyze the role of task similarity in learning and evaluate the performance gain when tasks are learned together rather than separately. In the supervised case, we derive a simple algorithm that attains the Bayes optimal performance.

翻译：本文考虑基于高斯混合模型（GMM）的半监督多任务学习。利用统计物理学方法，我们计算了高维大数据情境下每个任务的渐近贝叶斯风险，并据此分析任务相似性在学习中的作用，评估任务联合学习相较于独立学习的性能增益。在监督学习情形下，我们推导出一种可达到贝叶斯最优性能的简单算法。