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.
