Beyond Convexity: Emerging Challenges in Data Science (17w5159)


(University of Wisconsin-Madison)

(Sandia National Laboratories)

(University of Wisconsin-Madison)

(University of Wisconsin-Madison)


The Casa Matemática Oaxaca (CMO) will host the "Beyond Convexity: Emerging Challenges in Data Science" workshop from October 22nd to October 27th, 2017.

Modern methods in machine learning have led to a renaissance in large-scale analytics that has sped scientific exploration, revolutionized advertising strategies, improved health care services, and contributed strongly to national security. Many of these methods are based on convex optimization, a class of problems that is easy to solve in a mathematical sense, and also feasible in a practical sense, even for enormous data sets. Increasingly, data scientists are encountering problems that are not convex, and these are posing significant challenges for the current solver methodology. In general, algorithms for nonconvex problems may get stuck at suboptimal points that are not useful from a data analysis viewpoint. By taking account of the special properties of problems in data analysis, we can do better for a few specific problems, guaranteeing that the nonconvex algorithm is highly likely to produce a useful solution in reasonable amount of time.

Building on the good results obtained so far in some special cases, our challenge is to develop nonconvex optimization algorithms that work well in a large range of machine learning settings. Participants in the workshop will map the landscape of nonconvex data science problems, identifying problem structures, statistical properties, and optimization algorithms that allow these problems to be solved efficiently. The workshop will bring together researchers from machine learning, optimization, signal processing, statistics, industrial engineering, and applied mathematics, who will work together in this exciting interdisciplinary endeavor.

The Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, are collaborative Canada-US-Mexico ventures that provide an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry.

The research station in Banff is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT). The research station in Oaxaca is funded by CONACYT.