Graph-based Learning and Inference for Sparse Regularized Techniques

机器学习是一个非常活跃的跨学科研究领域，与统计学、最优化和计算机科学密切相关。这个项目的目标是开发几种用于解决高维问题的尖端机器学习技术。该团队计划开发估计复杂图形的新技术，并利用最近开发的一些优化工具，为稀疏回归方法建立推理程序。本项目将开发的技术在许多学科中都有广泛的应用。这类应用有助于促进统计学、运筹学和生物信息学之间的跨学科研究。将有几个学生参与研究活动。许多机器学习技术都符合正则化框架。该项目将开发几种新的正规化方法。特别是，该团队将使用稀疏的正则化工具进行复杂的图形模型估计。此外，该团队将通过将套索问题重新表述为最优化中的随机变分不等式，为稀疏正则化回归方法(如套索)建立新的推理工具。将向统计界介绍最先进的优化技术。研究人员致力于为所设计的方法建立理论性质和有效的计算工具。在不同学科的应用将有助于从这些学科中产生新的知识和灵感。

Machine learning is a very active area of interdisciplinary research, closely related to statistics, optimization, and computer science. The goal of this project is to develop several cutting-edge machine learning techniques for solving high dimensional problems. The team plans to develop new techniques for estimating complex graphs and to establish inference procedures for sparse regression methods, using some recently developed tools in optimization. Techniques to be developed in this project have a wide range of applications in many disciplines. Such applications help to promote interdisciplinary research among statistics, operations research, and bioinformatics. Several students will be involved in the research activities.Many machine learning techniques fit in the regularization framework. This project will develop several new regularized methods. In particular, the team will use sparse regularized tools for complex graphical model estimation. Furthermore, the team will build a new inference tool for sparse regularized regression methods such as the LASSO, by reformulating the LASSO problem as a stochastic variational inequality in optimization. State-of-the-art techniques in optimization will be introduced to the statistical community. The researchers are committed to establishing both theoretical properties and efficient computational tools for the designed methods. Applications in various disciplines will help to generate new knowledge and inspirations from those disciplines.