Unifying Weak Supervision Methods and the Fundamentals of Matrix-vector Multiply
Abstract
The proposed research will focus on capturing the rich structure, present in a number of useful matrices anddistributions, as well as the complex dynamics that occur in optimization, inference, asynchronous systems and their interactions. To this end, families of orthogonal polynomials provide a powerful toolbox. Capturing these structures and dynamics exactly will allow the team to manipulate them to create faster linear algebra, inference, and optimization algorithms and systems. Studying the interactions will provide an understanding of the important tradeoffs and optimally tune complex systems.Today, only certain classes of structures are studied. For example, linear algebraic approaches are dominated by lowrank and sparse matrices; here, a more general class of matrices will be studied that allow for fast operations, though they are not low-rank and sparse. Furthermore, by using exact tools, instead of classic loose bounds, exact dynamics can be obtained.This research team has successfully characterized new kinds of structure in linear algebra and inference. Newconnections between system and optimization dynamics have also been identified. Given our group s expertise, these refined characterizations can be used to improve algorithms and systems, as well as push for new theory. The results of this research will identify specific structures, for example, recurrence width and hierarchy width. A number of interesting cases fall within these two classes, but not all. Identifying all these cases that require new theoretical work is part of the research plan.This work will provide an understanding of the fundamental limitations and tradeoffs of commonly used data tools. This understanding can then be used to build optimally tuned systems that require few resources and very little expert intervention.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Mar 03, 2017
- Source ID
- N000141712266
Entities
People
- Christopher Ré
Organizations
- Office of Naval Research
- Stanford University
- United States Navy