NSF Award
1838131
The dramatic increases in our abilities to observe massive amounts of measurements coming from distributed and disparate high-resolution sensors have been instrumental in enhancing our understanding of many physical phenomena. Signal processing has been the primary driving force in this knowledge of the unseen from observed measurements. However, in the last decade, the exponential increase in observations has outpaced our computing abilities to process, understand, and organize this massive but useful information. In this project the investigators plan to blend efficient hashing algorithms with Randomized Numerical Linear Algebra, which can overcome these computational barriers. The project will engage diverse graduate and undergraduate students in computer science, statistics, ECE, and applied mathematics both at UCB and Rice. The efforts of this project will also be utilized to push data science for social good, through collaborations with a human rights data analysis group in leveraging hashing algorithms to reduce human efforts in estimating the extent of war crimes. The results of the project will be made available to a wide audience through OpenStax CNX, which will to disseminate course materials free-of-charge to anyone in the world and thereby foster the growth of vibrant communities around the subject.<br/><br/>This project will achieve two complementary goals: first, extend the foundations of RandNLA by tailoring randomization directly towards downstream end goals provided by the underlying problem, rather than intermediate matrix approximations goals; and second, use the statistical and optimization insights obtained from these downstream applications to transform and extend the foundations of RandNLA. The investigators will propose and extend several fundamental ideas, including probabilistic hashing, sketching, streaming, sampling, leverage scores, and random projections, to make SP significantly resource-frugal. Precise mathematical quantification of these tradeoffs will be provided.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
