Rina F. Barber, Ph.D. - US grants

This Research Training Group (RTG) project supports creation of a dynamic, interactive, and vertically integrated community of students and researchers working together in computational and applied mathematics and statistics. The activity recognizes the ways in which applied mathematics and statistics are becoming increasingly integrated. For example, mechanistic models for physical problems that reflect underlying physical laws are being combined with data-driven approaches in which statistical inference and optimization play key roles. These developments are transforming research agendas throughout statistics and applied mathematics, with fundamental problems in analyzing data leading to new areas of mathematical and statistical research. A result is a growing need to train the next generation of statisticians and computational and applied mathematicians in new ways, to confront data-centric problems in the natural and social sciences.

The research and educational activities of the project lie at the interface of statistics, computation, and applied mathematics. The research includes investigations in chemistry and molecular dynamics, climate science, computational neuroscience, convex and nonlinear optimization, machine learning, and statistical genetics. The research team is made up of a diverse group of twelve faculty, including researchers at Toyota Technological Institute at Chicago and Argonne National Laboratory. The RTG is centered on vertically integrated research experiences for students, and includes innovations in both undergraduate and graduate education. These include the formation of working groups of students and postdocs to provide an interactive environment where students can actively explore innovations in computation, mathematics, and statistics in a broad range of disciplines. Post-docs will assume leadership roles in mentoring graduate students and advanced undergraduates. Participants in the RTG will receive an educational experience that provides them with strong preparation for positions in industry, government, and academics, with an ability to adopt approaches to problem solving that are drawn from across the computational, mathematical, and statistical sciences.

Modern large-scale data sets arising in the physical and biological sciences often exhibit complex features that do not fit into the framework of existing methodologies, preventing the information in the gathered data from being fully utilized. In medical imaging, computed tomography (CT) scans and positron emission tomography (PET) scans are often best represented with models that are complex, beyond the scope of most available computational approaches, as existing methodology and theoretical analysis are mostly restricted to simpler classes of optimization problems. Since CT and PET scans come with a cost of a small radiation dose to the patient, better models for the data obtained by these imaging devices would result in a better tradeoff between the risk due to radiation and the benefit of obtaining a precise image for effective diagnosis and treatment. This research project will study a broad framework for complex optimization problems, applicable to medical imaging and across a range of problems in the physical and biological sciences, providing concrete methods and guarantees for many problems arising in these fields. The developed tools will be implemented on specific image reconstruction problems in CT and PET imaging, through collaborations with medical imaging researchers who will provide actual scan data, with the goal of enabling greater diagnostic accuracy for these popular clinical tools. Methods and code developed under this project will all be made publicly available. Throughout, the investigator will mentor students interested in working at the intersection of high-dimensional statistics, optimization, and medical imaging, and will increase interaction and communication across these fields through new courses and new collaborations.

Statistical problems arising in many modern applied fields often exhibit a range of challenging features, including non-convexity and non-differentiability, that pose significant challenges for high dimensional optimization and theoretical analysis. The proposed research will explore complex non-convex optimization and identifiability problems to develop methodology and theory for a broad range of problems facing applied researchers in practice. The research will study and develop algorithms that adapt techniques such as sparse or low-rank optimization, primal/dual methods, and alternating minimization or alternating descent, with the aim of achieving efficient empirical performance and broad theoretical convergence guarantees. The resulting methods will be adapted to address concrete problems in medical imaging, where noisy side information must be incorporated into the reconstructed image, and where the image representation is confounded by additional parameters modeling the imaging device.

Data science is making an enormous impact on science and society, but its success is uncovering pressing new challenges that stand in the way of further progress. Outcomes and decisions arising from many machine learning processes are not robust to errors and corruption in the data; data science algorithms are yielding biased and unfair outcomes, as concerns about data privacy continue to mount; and machine learning systems suited to dynamic, interactive environments are less well developed than corresponding tools for static problems. Only by an appeal to the foundations of data science can we understand and address challenges such as these. Building on the work of three TRIPODS Phase I institutes, the new Institute for Foundations of Data Science (IFDS) brings together researchers from the Universities of Washington, Wisconsin-Madison, California-Santa Cruz, and Chicago, organized around the goal of tackling these critical issues. Members of IFDS have complementary strengths in the TRIPODS disciplines of mathematics, statistics, and theoretical computer science, and a proven record of collaborating to push theoretical boundaries by synthesizing knowledge and experience from diverse areas. Students and postdoctoral members of IFDS will be trained to be fluent in the languages of several disciplines, and able to bridge these communities and perform transdisciplinary research in the foundations of data science. In concert with its research agenda, IFDS will engage the data science community through workshops, summer schools, and hackathons. Its diverse leadership, committed to equity and inclusion, proposes extensive plans for outreach to traditionally underrepresented groups. Governance, management, and evaluation of the institute will build on the successful and efficient models developed during Phase I.

To address critical issues at the cutting edge of data science research, IFDS will organize its research around four core themes. The complexity theme will synthesize various notions of complexity from multiple disciplines to make breakthroughs in the analysis of optimization and sampling methods, develop tools for assessing the complexity of data models, and seek new methods with better complexity properties, to make complexity a more powerful tool for understanding and inventing algorithms in data science. The robustness theme considers data that contains errors or outliers, possibly due to an adversary, and will design methods for data analysis and prediction that are robust in the face of these errors. The theme on closed-loop data science tackles the issues of acquiring data in ways that reveal the information content of the data efficiently, using strategic and sequential policies that leverage information gathered already from past data. The theme on ethics and algorithms addresses issues of fairness and bias in machine learning, data privacy, and causality and interpretability. The four themes intersect in many ways, and most IFDS researchers will work in two or more of them. By making concerted progress on these fundamental fronts, IFDS will lower several of the barriers to better understanding of data science methodology and to its improved effectiveness and wider relevance to application areas. Additionally, IFDS will organize and host activities that engage the data science community at all levels of seniority. Annual workshops will focus on the critical issues identified above and others that are sure to arise over the next five years. Comprehensive plans for outreach and education will draw on previous experience of the Phase I institutes and leverage institutional resources at the four sites. Collaborations with domain science researchers in academia, national laboratories, and industry, so important in illuminating issues in the fundamentals of data science, will continue through the many channels available to IFDS members, including those established in the TRIPODS+X program. Relationships with other institutes at each IFDS site will further extend the impact of IFDS on domain sciences and applications.

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.