Fiscal Year	2018
Division	Graduate School of Operational & Information Sciences
Department	Operations Research
Investigator(s)	Royset, Johannes O.
Sponsor	Defense Advanced Research Projects Agency (DoD)
Summary	The rapidly developing area of data science is addressing many important challenges in high-dimensional statistics. However, in the age of "big data," it is easily forgotten that despite the massive amounts of data collected, estimation of a particular quantity of interest still often suffers from too few relevant observations. A reason can be that the statistical models we hope to fit are large-scale and therefore highly data intensive. The proposed work aims to develop theory and algorithms for infinite-dimensional optimization while addressing such Small-Data Problems in nonparametric statistics. In addition to the specific application domain, we plan to fundamentally advance the general principles of mathematical optimization through new paradigms for infinite-dimensional problems that tackle challenges of dimensionality, approximations, and error quantification. The proposed study will open new avenues for statistical modeling and even the possibility to obtain data-free estimators that only rely on auxiliary and subjective information and not on data. The proposed work will also lay the foundation for solving numerous other infinite-dimensional optimization problems such as those in shape design, optimal control, policy optimization, and other dynamical problems.
Keywords	Data Analytics Data Science Optimization
Publications	Publications, theses (not shown) and data repositories will be added to the portal record when information is available in FAIRS and brought back to the portal
Data	Publications, theses (not shown) and data repositories will be added to the portal record when information is available in FAIRS and brought back to the portal