Atd Collaborative Research: Theory and Algorithms for High Dimensional Learning
The investigators and their collaborators study how to organize and query high dimensional data in order to extract relevant content while avoiding the so-called curse of dimensionality. The team is developing new analytical and numerical methods based on sparsity, adaptivity, and variable reduction. The focus is placed on developing a coherent theory that results in sophisticated state-of-the-art numerical algorithms that can be applied in a variety of settings. This activity is a critical component of many scientific problems since it complements and supports the scientific methods of theory, experimentation, and simulation. A setting of particular interest to this project is learning tasks such as regression and classification. The research team is developing quantifiable frameworks and algorithms for learning that systematically break down the high dimensional barriers and exploit empirical data collections. Many scientic problems, vital to the security, economy, and health of our nation, are so complex that they challenge this nation''s most sophisticated computational resources. Examples occur in modeling physical and biological systems, e.g. in atmospheric modeling; in optimal design (optimal control and shape optimization); and also in understanding social networks such as those that occur in threat detection. The complexity of these problems prohibits the use of traditional off-the-shelf computational techniques for their solution. This research team develops new computational tools that lead to state of the art algorithms for detecting and the capturing critical information held in the solution of such complex systems. An emphasis in this project is the processing of data that arise in threat detection, damage assessment, and containment. This requires the simultaneous analysis of data obtained from different modalities and a variety of sensors. The new algorithms are applied, for example, to identify and track the migration of airborne biological and chemical contaminants. Another application area is the development of new approaches to high dimensional problems related to gene sequencing.