Research Training Group: Data-Oriented Mathematical and Statistical Sciences
Acknowledgment of the challenges of extracting useful information from ever-growing torrents and oceans of raw data has become nearly ubiquitous over the past decade. Mathematical and statistical reasoning are central to addressing these challenges, and the mathematical sciences have established an impressive track record in providing methodology for “big data” problems as they have emerged in recent decades. The ASU Research Training Group (RTG) program is sponsored by the National Science Foundation to keep pace with these challenges. The program includes training in three areas:
- Statistics is by its nature concerned with analysis of data. Concepts like development of sufficient statistics for hypothesis tests and identifying estimators for critical model parameters that make efficient use of collected data remain among the most powerful in the modern arsenal.
- Computational Mathematics has been primarily responsible for algorithmic speedups that have rivaled Moore's law advances in processing technology in enabling meaningful processing of data. It also provides a bridge between ``exact'' solutions and heuristic algorithms by providing rigorous approximate solutions with certificates of fidelity and complexity.
- Harmonic Analysis has underpinned most of the advances in data compression over the past thirty years, providing mechanisms for dimensionality reduction through parsimonious representation of high-dimensional data in judiciously chosen bases or frames. More recently, this area of mathematics has been instrumental in advancing ways to identify and exploit compressibility, not just in through low-dimensional subspaces of linear spaces but also by capitalizing on other kinds of low-dimensional structure.
The RTG program fosters integration across these areas to cultivate mathematical scientists who have skills in all three of them and can furthermore understand how to draw on concepts from multiple areas in addressing data-oriented problems. Examples of research questions to be addressed by the synergy of these disciplines include (but are not limited to):
- finding and analyzing efficient and adaptive data collection strategies in sequential experimental design
- reconstructing signals and/or images from incomplete and/or noisy data sources
- devising measurement and other data collection strategies that optimize the value of the data in subsequent statistical tests or estimators
All ASU undergraduate students, graduate students, and postdoctoral fellows are welcome to participate in the RTG seminar, which will include both research and professional development components.
Undergraduate students, graduate students, and postdoctoral fellows participating in the RTG program will have the opportunity to complete some research activity at an off-site location, typically during the summer at a national research laboratory or medical center. This will give participants a chance to collaborate with research from diverse backgrounds and other scientific disciplines on real data-data oriented problems.
Those interested in participating should contact Rodrigo Platte.
Funding is provided by the National Science Foundation and the School of Mathematical and Statistical Sciences.