The research in this proposal lies at the boundary of statistics and machine learning, with the underlying theme of nonparametric inference for high-dimensional data. Nonparametric inference refers to statistical methods that learn from data without imposing strong assumptions. The project will develop the mathematical foundations of learning sparse functions in high-dimensional data, and will also develop scalable, practical algorithms that address the statistical and computational curses of dimensionality. The project will rigorously develop the idea that it is possible to overcome these curses if, hidden in the high-dimensional problem, there is low-dimensional structure. The focus of the project will be on five technical aims: (1) Develop practical methods for high-dimensional nonparametric regression (2) Develop theory for learning when the dimension increases with sample size (3) Develop theory that incorporates computational costs into statistical risk (4) Develop methods for sparse, highly structured models (5) Develop methods for data with a low intrinsic dimensionality. These aims target the advancement of both statistical theory and computer science, and the interdisciplinary team for the project includes a statistician (Wasserman), a computer scientist (Lafferty), and a physicist who is now in a statistics department (Lee).
