基于Safe screening的多任务稀疏学习理论与算法的研究

多任务学习广泛存在于我们现实生活中，它通过共享多个相关任务之间的信息提升了学习性能。但随着数据规模的增大会消耗大量的运算时间和内存。为了克服上述问题，本项目以优化理论为基础，构建基于safe screening的多任务稀疏学习理论和快速求解方法。通过变分不等式、对偶间隙、目标函数的强凸性等理论构建安全的筛选准则，删除训练集中冗余的样本或特征，缩减优化问题的规模，加快求解速度。而且我们的筛选准则可以从理论上保证得到与原问题完全相同的解。主要包括:(1)针对各类稀疏的多任务模型的特点，分别构建安全的样本筛选准则、特征筛选准则、样本与特征同时筛选准则，缩减问题的规模；(2)构建基于Safe screening的嵌入式序列方法、参数自动选择框架和结合有效集的快速求解方法，加速求解速度；(3)将构建的模型应用到301医院的糖尿病医疗诊断中，提高诊断效率。

Multi-task learning is widespread in our real life. It can improve the generalization performance by sharing the related information among all tasks. However, it costs large amount of running time and storage with increasing of data. To effectively address this problem, based on optimization theory, safe screening rule for the multi-task sparse learning and fast solving method are researched in this project. By variational inequality、duality gap and strong convexity of objective function, the proposed safe screening rule can safely discard most redundant samples or features before solving the optimization problem、reduce the scale of the optimization problems and improve the learning speed. More importantly, it guarantees that we can obtain the exactly same solution as the original optimization problem in theory. The following main contents are included in this project: (1) Construct safe sample screening rule, safe feature screening rule, and simultaneous safe sample and feature elimination rule for the sparse multi-task learning models in order to reduce the scale of optimization problem. (2) Propose some fast solving algorithms including an embedded sequential safe screening, automatic parameter selection and working set to further improve the learning speed. (3) Finally, we apply our proposed methods to the medical diagnosis of diabetes from Chinese People's Liberation Army General Hospital to improve the diagnosis efficiency.