Machine Learning, Nonlinear PDEs, and Biomedical Applications

This project aims to provide a novel perspective on machine learning and explore its impact on biomedical research. Online machine learning has the benefit that it allows for sequential data processing which can ultimately support decision making - key topics in an era of shared economy, cybersecurity, and big data. The investigator plans to develop new approaches and the underlying theory for online machine learning in the context of game theory and partial differential equations that have a range of applications, including finance, medicine, and spam detection. Furthermore, in collaboration with biomedical researchers, the investigator will analyze the performance of algorithms for predicting unknown medical data from images of the human body, which is used in obesity, metabolism, and nutrition research. Undergraduate and graduate students will be trained on some of the latest machine learning algorithms as part of this project, preparing them for careers both in research and in industry jobs. A fundamental challenge in online machine learning is the increasing complexity of existing algorithms' implementations. Furthermore, most algorithms are not tailored to specific use cases and thus provide suboptimal solutions. This work will provide alternatives to the currently existing online machine learning approaches by introducing ideas and techniques from partial differential equations and optimal control theory. By targeting specific models and using scaling limits, these continuous methods are expected to provide a new framework to find and analyze novel, proved-to-be-optimal algorithms for big data. This research involves a novel approach for using continuous tools to solve discrete problems, providing a fresh view on classically discrete frameworks. A novel game-theoretic interpretation of the optimal strategies can also inform properties of the corresponding partial differential equation solution. This work also entails the analysis of biomedical data using various regression, supervised learning, and semi-supervised learning techniques. 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.